International Journal of Mathematics最新文献

{"title":"Seshadri constants on some flag bundles","authors":"Krishna Hanumanthu, Jagadish Pine","doi":"10.1142/s0129167x24500332","DOIUrl":"https://doi.org/10.1142/s0129167x24500332","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> be a smooth complex projective curve and let <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>E</mi></math></span><span></span> be a vector bundle on <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> which is not semistable. We consider a flag bundle <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>π</mi><mo>:</mo><mstyle><mtext mathvariant=\"normal\">Fl</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>E</mi><mo stretchy=\"false\">)</mo><mo>→</mo><mi>X</mi></math></span><span></span> parametrizing certain flags of fibers of <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>E</mi></math></span><span></span>. The dimensions of the successive quotients of the flags are determined by the ranks of vector bundles appearing in the Harder–Narasimhan filtration of <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>E</mi></math></span><span></span>. We compute the Seshadri constants of nef line bundles on <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">Fl</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>E</mi><mo stretchy=\"false\">)</mo></math></span><span></span>.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"45 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Automorphisms of moduli spaces of principal bundles over a smooth curve","authors":"Roberto Fringuelli","doi":"10.1142/s0129167x24500368","DOIUrl":"https://doi.org/10.1142/s0129167x24500368","url":null,"abstract":"<p>For any almost-simple group <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span> over an algebraically closed field <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>k</mi></math></span><span></span> of characteristic zero, we describe the automorphism group of the moduli space of semistable <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span>-bundles over a connected smooth projective curve <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math></span><span></span> of genus at least <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mn>4</mn></math></span><span></span>. The result is achieved by studying the singular fibers of the Hitchin fibration. As a byproduct, we provide a description of the irreducible components of two natural closed subsets in the Hitchin basis: the divisor of singular cameral curves and the divisor of singular Hitchin fibers.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Killing spinors and hypersurfaces","authors":"Diego Conti, Romeo Segnan Dalmasso","doi":"10.1142/s0129167x24500356","DOIUrl":"https://doi.org/10.1142/s0129167x24500356","url":null,"abstract":"<p>We consider spin manifolds with an Einstein metric, either Riemannian or indefinite, for which there exists a Killing spinor. We describe the intrinsic geometry of nondegenerate hypersurfaces in terms of a PDE satisfied by a pair of induced spinors, akin to the generalized Killing spinor equation.</p><p>Conversely, we prove an embedding result for real analytic pseudo-Riemannian manifolds carrying a pair of spinors satisfying this condition.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"130 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A geometric perspective on plus-one generated arrangements of lines","authors":"Anca Măcinic, Jean Vallès","doi":"10.1142/s0129167x24500344","DOIUrl":"https://doi.org/10.1142/s0129167x24500344","url":null,"abstract":"<p>We give a geometric characterization of plus-one generated projective line arrangements that are next-to-free. We present new succinct proofs, via associated line bundles, for some properties of plus-one generated projective line arrangements.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"19 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Harmonic metrics for the Hull–Strominger system and stability","authors":"M. Garcia-Fernandez, R. Gonzalez Molina","doi":"10.1142/s0129167x24410088","DOIUrl":"https://doi.org/10.1142/s0129167x24410088","url":null,"abstract":"<p>We investigate stability conditions related to the existence of solutions of the Hull–Strominger system with prescribed balanced class. We build on recent work by the authors, where the Hull–Strominger system is recasted using non-Hermitian Yang–Mills connections and holomorphic Courant algebroids. Our main development is a notion of <i>harmonic metric</i> for the Hull–Strominger system, motivated by an infinite-dimensional hyperKähler moment map and related to a numerical stability condition, which we expect to exist for families of solutions. We illustrate our theory with an infinite number of continuous families of examples on the Iwasawa manifold.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"30 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Contact instantons with Legendrian boundary condition: A priori estimates, asymptotic convergence and index formula","authors":"Yong-Geun Oh, Seungook Yu","doi":"10.1142/s0129167x24500198","DOIUrl":"https://doi.org/10.1142/s0129167x24500198","url":null,"abstract":"<p>In this paper, we establish nonlinear ellipticity of the equation of contact instantons with Legendrian boundary condition on punctured Riemann surfaces by proving the a priori elliptic coercive estimates for the contact instantons with Legendrian boundary condition, and prove an asymptotic exponential <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>C</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span><span></span>-convergence result at a puncture under the uniform <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span><span></span> bound. We prove that the asymptotic charge of contact instantons at the punctures <i>under the Legendrian boundary condition</i> vanishes. This eliminates the phenomenon of the appearance of <i>spiraling cusp instanton along a Reeb core</i>, which removes the only remaining obstacle towards the compactification and the Fredholm theory of the moduli space of contact instantons in the open string case, which plagues the closed string case. Leaving the study of <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span><span></span>-estimates and details of Gromov-Floer-Hofer style compactification of contact instantons to [27], we also derive an index formula which computes the virtual dimension of the moduli space. These results are the analytic basis for the sequels [27]–[29] and [36] containing applications to contact topology and contact Hamiltonian dynamics.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"344 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Regular and rigid curves on some Calabi–Yau and general-type complete intersections","authors":"Ziv Ran","doi":"10.1142/s0129167x24420011","DOIUrl":"https://doi.org/10.1142/s0129167x24420011","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> be either a general hypersurface of degree <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi><mo stretchy=\"false\">+</mo><mn>1</mn></math></span><span></span> in <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℙ</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span> or a general <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mn>2</mn><mo>,</mo><mi>n</mi><mo stretchy=\"false\">)</mo></math></span><span></span> complete intersection in <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℙ</mi></mrow><mrow><mi>n</mi><mo stretchy=\"false\">+</mo><mn>1</mn></mrow></msup><mo>,</mo><mi>n</mi><mo>≥</mo><mn>4</mn></math></span><span></span>. We construct balanced rational curves on <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> of all high enough degrees. If <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi><mo>=</mo><mn>4</mn></math></span><span></span> or <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi><mo>=</mo><mn>1</mn></math></span><span></span>, we construct rigid curves of genus <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi></math></span><span></span> on <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> of all high enough degrees. As an application we construct some rigid bundles on Calabi–Yau threefolds. In addition, we construct some low-degree balanced rational curves on hypersurfaces of degree <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi><mo stretchy=\"false\">+</mo><mn>2</mn></math></span><span></span> in <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℙ</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span>.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"24 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Explicit universal bounds for squeezing functions of (ℂ-)convex domains","authors":"Gautam Bharali, Nikolai Nikolov","doi":"10.1142/s0129167x24500319","DOIUrl":"https://doi.org/10.1142/s0129167x24500319","url":null,"abstract":"<p>In this paper, we prove two separate lower bounds — one for nondegenerate convex domains and the other for nondegenerate <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>ℂ</mi></math></span><span></span>-convex (but not necessarily convex) domains — for the squeezing function that hold true for all domains in <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℂ</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span>, for a fixed <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi><mo>≥</mo><mn>2</mn></math></span><span></span>, of the stated class. We provide explicit expressions in terms of <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi></math></span><span></span> for these estimates.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"72 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140808856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Knot concordance invariants from Seiberg–Witten theory and slice genus bounds in 4-manifolds","authors":"David Baraglia","doi":"10.1142/s0129167x24500320","DOIUrl":"https://doi.org/10.1142/s0129167x24500320","url":null,"abstract":"<p>We construct a new family of knot concordance invariants <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>𝜃</mi></mrow><mrow><mo stretchy=\"false\">(</mo><mi>q</mi><mo stretchy=\"false\">)</mo></mrow></msup><mo stretchy=\"false\">(</mo><mi>K</mi><mo stretchy=\"false\">)</mo></math></span><span></span>, where <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>q</mi></math></span><span></span> is a prime number. Our invariants are obtained from the equivariant Seiberg–Witten–Floer cohomology, constructed by the author and Hekmati, applied to the degree <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>q</mi></math></span><span></span> cyclic cover of <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span> branched over <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>K</mi></math></span><span></span>. In the case <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>q</mi><mo>=</mo><mn>2</mn></math></span><span></span>, our invariant <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>𝜃</mi></mrow><mrow><mo stretchy=\"false\">(</mo><mn>2</mn><mo stretchy=\"false\">)</mo></mrow></msup><mo stretchy=\"false\">(</mo><mi>K</mi><mo stretchy=\"false\">)</mo></math></span><span></span> shares many similarities with the knot Floer homology invariant <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ν</mi></mrow><mrow><mo stretchy=\"false\">+</mo></mrow></msup><mo stretchy=\"false\">(</mo><mi>K</mi><mo stretchy=\"false\">)</mo></math></span><span></span> defined by Hom and Wu. Our invariants <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>𝜃</mi></mrow><mrow><mo stretchy=\"false\">(</mo><mi>q</mi><mo stretchy=\"false\">)</mo></mrow></msup><mo stretchy=\"false\">(</mo><mi>K</mi><mo stretchy=\"false\">)</mo></math></span><span></span> give lower bounds on the genus of any smooth, properly embedded, homologically trivial surface bounding <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>K</mi></math></span><span></span> in a definite <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mn>4</mn></math></span><span></span>-manifold with boundary <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span>.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"127 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A refinement of the LMO invariant for 3-manifolds with the first Betti number 1","authors":"Tomotada Ohtsuki","doi":"10.1142/s0129167x24500204","DOIUrl":"https://doi.org/10.1142/s0129167x24500204","url":null,"abstract":"<p>It is known that the LMO invariant of 3-manifolds with positive first Betti numbers is relatively weak and can be determined by “(semi-)classical” invariants such as the cohomology ring, the Alexander polynomial, and the Casson–Walker–Lescop invariant.</p><p>In this paper, we formulate a refinement of the LMO invariant for 3-manifolds with the first Betti number 1. It dominates the perturbative SO(3) invariant of such 3-manifolds, which is the power series invariant formulated by the arithmetic perturbative expansion of the quantum SO(3) invariants of such 3-manifolds. As the 2-loop part of the refinement of the LMO invariant, we define the 2-loop polynomial of such 3-manifolds. Further, as the <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>𝔰</mi><msub><mrow><mi>𝔩</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span><span></span> reduction at large <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>m</mi></math></span><span></span> limit of the <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>ℓ</mi></math></span><span></span>-loop part of the refinement of the LMO invariant for <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>ℓ</mi><mo>≤</mo><mn>5</mn></math></span><span></span>, we formulate an <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>ℓ</mi></math></span><span></span>-variable polynomial invariant of such 3-manifolds whose Alexander polynomial is constant.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"44 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}