Bulletin des Sciences Mathematiques最新文献

{"title":"The existence of positive periodic solutions about generalized hematopoiesis model","authors":"Jia Yuan ,&nbsp;Lishan Liu ,&nbsp;Haibo Gu ,&nbsp;Yonghong Wu","doi":"10.1016/j.bulsci.2025.103638","DOIUrl":"10.1016/j.bulsci.2025.103638","url":null,"abstract":"<div><div>This paper focuses on the generalized hematopoietic model with multiple variable delays and multiple exponents. Using the fixed point theorem of cone expansion and compression, it is proved that the hematopoiesis model in the sup-linear or sub-linear case must have a positive periodic solution. And it is deduced that there are two positive periodic solutions for the hematopoietic model when it has both sup-linear and sub-linear terms. In addition, several examples of the numerical simulations are given in this paper for illustration.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103638"},"PeriodicalIF":1.3,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143859826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Seshadri constants of M‾0,n","authors":"Shripad M. Garge ,&nbsp;Arghya Pramanik ,&nbsp;Aditya Subramaniam","doi":"10.1016/j.bulsci.2025.103639","DOIUrl":"10.1016/j.bulsci.2025.103639","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>n</mi></mrow></msub></math></span> be the moduli space of stable rational <em>n</em>-pointed curves for <span><math><mi>n</mi><mo>≥</mo><mn>5</mn></math></span>. We estimate lower bounds for Seshadri constants of nef <span><math><mi>Q</mi></math></span>-line bundles at arbitrary points on <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>n</mi></mrow></msub></math></span> for <span><math><mn>5</mn><mo>≤</mo><mi>n</mi><mo>≤</mo><mn>7</mn></math></span>. Our results for <span><math><mi>n</mi><mo>=</mo><mn>5</mn></math></span> generalise some results of Taro Sano (2014). We also estimate lower bounds for Seshadri constants of nef Keel divisors at arbitrary points on <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>n</mi></mrow></msub></math></span> for <span><math><mi>n</mi><mo>≥</mo><mn>8</mn></math></span>, assuming a conjecture describing the Mori cone of <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>n</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103639"},"PeriodicalIF":1.3,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143859827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Infinitesimal and tangential 16-th Hilbert problem on zero-cycles","authors":"J.L. Bravo ,&nbsp;P. Mardešić ,&nbsp;D. Novikov ,&nbsp;J. Pontigo-Herrera","doi":"10.1016/j.bulsci.2025.103634","DOIUrl":"10.1016/j.bulsci.2025.103634","url":null,"abstract":"<div><div>In this paper, given two polynomials <em>f</em> and <em>g</em> of one variable and a 0-cycle <em>C</em> of <em>f</em>, we consider the deformation <span><math><mi>f</mi><mo>+</mo><mi>ϵ</mi><mi>g</mi></math></span>. We define two functions: the <em>displacement function</em> <span><math><mi>Δ</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>ϵ</mi><mo>)</mo></math></span> and its first order approximation: the <em>abelian integral</em> <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span>.</div><div>The <em>infinitesimal</em> and <em>tangential 16-th Hilbert problem</em> for zero-cycles are problems of counting isolated regular zeros of <span><math><mi>Δ</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>ϵ</mi><mo>)</mo></math></span>, for <em>ϵ</em> small, or of <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span>, respectively.</div><div>We show that the two problems are not equivalent and find optimal bounds, in function of the degrees of <em>f</em> and <em>g</em>, for the infinitesimal and tangential 16-th Hilbert problem on zero-cycles. These two problems are the zero-dimensional analog of the classical infinitesimal and tangential 16-th Hilbert problems for vector fields in the plane.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103634"},"PeriodicalIF":1.3,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrigendum to: Half-integrality of line bundles on partial flag schemes of classical Lie groups","authors":"Takuma Hayashi","doi":"10.1016/j.bulsci.2025.103626","DOIUrl":"10.1016/j.bulsci.2025.103626","url":null,"abstract":"<div><div>In this note, I fix mistakes on the continuity arguments concerning the profinite topology of the Galois group of an infinite Galois extension of fields in my previous paper <span><span>[6]</span></span>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103626"},"PeriodicalIF":1.3,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143806592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Invariant p-complements normalized by the fixed point subgroup","authors":"Hangyang Meng ,&nbsp;Xingyu Zhang","doi":"10.1016/j.bulsci.2025.103635","DOIUrl":"10.1016/j.bulsci.2025.103635","url":null,"abstract":"<div><div>Let a group <em>A</em> act on a group <em>G</em> coprimely, i.e., <span><math><mo>(</mo><mo>|</mo><mi>A</mi><mo>|</mo><mo>,</mo><mo>|</mo><mi>G</mi><mo>|</mo><mo>)</mo><mo>=</mo><mn>1</mn></math></span>. We say that <em>G</em> is <em>A</em>-<em>p</em>-nilpotent if <em>G</em> has an <em>A</em>-invariant <span><math><mi>Hall</mi><mspace></mspace><msup><mrow><mi>p</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span>-subgroup normalized by <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span>. In this paper, we give some equivalent descriptions on <em>A</em>-<em>p</em>-nilpotence by analyzing the structure of minimal non-<em>A</em>-<em>p</em>-nilpotent groups. This is a follow-up work to A. Beltrán's research.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103635"},"PeriodicalIF":1.3,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143807280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global existence of strong solutions to the 3D incompressible magnetohydrodynamics equations with zero heat-conduction","authors":"Jinxia Liang ,&nbsp;Xinqiu Zhang","doi":"10.1016/j.bulsci.2025.103625","DOIUrl":"10.1016/j.bulsci.2025.103625","url":null,"abstract":"<div><div>In this paper, we study an initial-boundary value problem of three-dimensional inhomogeneous incompressible magnetohydrodynamics (MHD) fluids with vacuum, zero heat-conduction and density-temperature-dependent viscosity and magnetic diffusive coefficients. Based on the time-weighted a priori estimates, we establish the global existence and exponential decay properties of strong solutions under the conditions that the initial energy is suitably small.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103625"},"PeriodicalIF":1.3,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Perturbations of a system of general functional equations in several variables","authors":"Hamid Khodaei","doi":"10.1016/j.bulsci.2025.103624","DOIUrl":"10.1016/j.bulsci.2025.103624","url":null,"abstract":"<div><div>Pólya and Szegő <span><span>[53, Teil I, Aufgabe 99]</span></span> proved that every approximate sequence of reals is near an additive sequence. Bourgin <span><span>[11]</span></span> showed that every approximate ring homomorphism from a Banach algebra onto a unital Banach algebra is necessarily a ring homomorphism. We deal with Pólya-Szegő's result for a general functional equation and a system of general functional equations in several variables. To do this, we shall use a different direct method from the previous studies. In consequence, Bourgin's result for approximate homomorphisms and Lie homomorphisms on Banach algebras are discussed. Several examples for comparison with previous studies are included.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103624"},"PeriodicalIF":1.3,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subnormal transcendental meromorphic solutions of delay differential equations","authors":"Mengting Xia,&nbsp;Jianren Long,&nbsp;Xuxu Xiang","doi":"10.1016/j.bulsci.2025.103623","DOIUrl":"10.1016/j.bulsci.2025.103623","url":null,"abstract":"<div><div>The following two delay differential equations are studied,<span><span><span><math><mi>ω</mi><msup><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mrow><mi>k</mi></mrow></msup><munderover><mo>∑</mo><mrow><mi>μ</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>s</mi></mrow></munderover><msub><mrow><mi>e</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>(</mo><mi>z</mi><mo>)</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>)</mo><mo>+</mo><mi>a</mi><mo>(</mo><mi>z</mi><mo>)</mo><mfrac><mrow><msup><mrow><mi>ω</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mrow><mi>ω</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mfrac><mo>=</mo><mi>R</mi><mo>(</mo><mi>z</mi><mo>,</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>)</mo><mo>,</mo></math></span></span></span> and<span><span><span><math><mo>(</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>)</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>−</mo><mn>1</mn><mo>)</mo><mo>(</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>)</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>−</mo><mn>1</mn><mo>)</mo><mo>+</mo><mi>a</mi><mo>(</mo><mi>z</mi><mo>)</mo><mfrac><mrow><msup><mrow><mi>ω</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mrow><mi>ω</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mfrac><mo>=</mo><mi>R</mi><mo>(</mo><mi>z</mi><mo>,</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>)</mo><mo>,</mo></math></span></span></span></div><div>where <span><math><mi>k</mi><mo>≥</mo><mn>0</mn></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>1</mn></math></span>, <span><math><mi>s</mi><mo>≥</mo><mn>1</mn></math></span> are integers, <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, <span><math><mo>.</mo><mo>.</mo><mo>.</mo></math></span>, <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> are nonzero complex numbers, <span><math><mi>a</mi><mo>(</mo><mi>z</mi><mo>)</mo></math></span>, <span><math><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></span>, <span><math><mo>.</mo><mo>.</mo><mo>.</mo></math></span>, <span><math><msub><mrow><mi>e</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></span> are small with respect to <em>ω</em>, <span><math><mi>R</mi><mo>(</mo><mi>z</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> is rational in <em>ω</em> with small meromorphic coefficients with respect to <em>ω</em>. The necessary conditions for the existence of subnormal transcendental meromorphic solutions of the above two equations are obtained, which extend the previous results from Cao, Chen and Korhonen <span><span>[2]</span></span>, Halburd and Korhonen <span><span>[6]</span></span>, Korhonen and Liu <span><span>[12]</span></span>. Some examples are given to support these results.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103623"},"PeriodicalIF":1.3,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weighted Cesàro type operators between weighted Bergman spaces","authors":"Petros Galanopoulos ,&nbsp;Aristomenis G. Siskakis ,&nbsp;Ruhan Zhao","doi":"10.1016/j.bulsci.2025.103622","DOIUrl":"10.1016/j.bulsci.2025.103622","url":null,"abstract":"<div><div>Let <span><math><mi>D</mi></math></span> be the open unit disk in the complex plane <span><math><mi>C</mi></math></span>. Let <em>μ</em> be a positive Borel measure on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. If <span><math><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is an analytic function in <span><math><mi>D</mi></math></span>, we consider for <span><math><mi>β</mi><mo>&gt;</mo><mn>0</mn></math></span> the following weighted Cesàro type operator<span><span><span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>μ</mi><mo>,</mo><mi>β</mi></mrow></msub><mo>(</mo><mi>f</mi><mo>)</mo><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></munderover><msub><mrow><mi>μ</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>n</mi></mrow></munderover><mfrac><mrow><mi>Γ</mi><mo>(</mo><mi>n</mi><mo>−</mo><mi>k</mi><mo>+</mo><mi>β</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mi>k</mi><mo>)</mo><mo>!</mo><mspace></mspace><mi>Γ</mi><mo>(</mo><mi>β</mi><mo>)</mo></mrow></mfrac><msub><mrow><mi>a</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><mspace></mspace><mi>z</mi><mo>∈</mo><mi>D</mi><mo>,</mo></math></span></span></span> where <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is the <em>n</em>-th moment of <em>μ</em> given by <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><munder><mo>∫</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></munder><msup><mrow><mi>t</mi></mrow><mrow><mi>n</mi></mrow></msup><mspace></mspace><mi>d</mi><mi>μ</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span>. We characterize boundedness of the weighted Cesàro type operator <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>μ</mi><mo>,</mo><mi>β</mi></mrow></msub></math></span> from the weighted Bergman space <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span> to <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow><mrow><mi>q</mi></mrow></msubsup></math></span> for <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mi>q</mi><mo>&lt;</mo><mo>∞</mo></math></span>. Our method relies on a representation of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>μ</mi><mo>,</mo><mi>β</mi></mrow></msub></math></span> as an integral operator with a kernel and a generalized Schur's test.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103622"},"PeriodicalIF":1.3,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On character variety of Anosov representations","authors":"Krishnendu Gongopadhyay,&nbsp;Tathagata Nayak","doi":"10.1016/j.bulsci.2025.103621","DOIUrl":"10.1016/j.bulsci.2025.103621","url":null,"abstract":"<div><div>Let Γ be the fundamental group of a <em>k</em>-punctured, <span><math><mi>k</mi><mo>≥</mo><mn>0</mn></math></span>, closed connected orientable surface of genus <span><math><mi>g</mi><mo>≥</mo><mn>2</mn></math></span>. We show that the character variety of the <span><math><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><msup><mrow><mi>Q</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math></span>-Anosov irreducible representations, resp. the character variety of the <span><math><mo>(</mo><msup><mrow><mi>P</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><msup><mrow><mi>P</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math></span>-Anosov Zariski dense representations of Γ into <span><math><mrow><mi>SL</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>, is a complex manifold of complex dimension <span><math><mo>(</mo><mn>2</mn><mi>g</mi><mo>+</mo><mi>k</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>1</mn><mo>)</mo></math></span>. For <span><math><mi>Γ</mi><mo>=</mo><msub><mrow><mi>π</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>)</mo></math></span>, we also show that these character varieties are holomorphic symplectic manifolds.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103621"},"PeriodicalIF":1.3,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}