{"title":"Automorphism and cohomology II: Complete intersections","authors":"Xi Chen, Xuanyu Pan, Dingxin Zhang","doi":"10.1142/s0129167x24500289","DOIUrl":"https://doi.org/10.1142/s0129167x24500289","url":null,"abstract":"<p>We prove that the automorphism group of a general complete intersection <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> in <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℂ</mi><mi>ℙ</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span> is trivial with a few well-understood exceptions. We also prove that the automorphism group of a complete intersection <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> acts on the cohomology of <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> faithfully with a few well-understood exceptions.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"118 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798940","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 blowing-up formula for the intersection cohomology of the moduli of rank 2 Higgs bundles over a curve with trivial determinant","authors":"Sang-Bum Yoo","doi":"10.1142/s0129167x24500228","DOIUrl":"https://doi.org/10.1142/s0129167x24500228","url":null,"abstract":"<p>We prove that a blowing-up formula for the intersection cohomology of the moduli space of rank <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mn>2</mn></math></span><span></span> Higgs bundles over a curve with trivial determinant holds. As an application, we derive the Poincaré polynomial of the intersection cohomology of the moduli space under a technical assumption.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"2 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613252","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":"Equivariant localization in the theory of Z-stability for Kähler manifolds","authors":"Alexia Corradini","doi":"10.1142/s0129167x24500265","DOIUrl":"https://doi.org/10.1142/s0129167x24500265","url":null,"abstract":"<p>We apply equivariant localization to the theory of <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>Z</mi></math></span><span></span>-stability and <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>Z</mi></math></span><span></span>-critical metrics on a Kähler manifold <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>X</mi><mo>,</mo><mi>α</mi><mo stretchy=\"false\">)</mo></math></span><span></span>, where <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi></math></span><span></span> is a Kähler class. We show that the invariants used to determine <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>Z</mi></math></span><span></span>-stability of the manifold, which are integrals over test configurations, can be written as a product of equivariant classes, hence equivariant localization can be applied. We also study the existence of <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>Z</mi></math></span><span></span>-critical Kähler metrics in <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi></math></span><span></span>, whose existence is conjectured to be equivalent to <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>Z</mi></math></span><span></span>-stability of <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>X</mi><mo>,</mo><mi>α</mi><mo stretchy=\"false\">)</mo></math></span><span></span>. In particular, we study a class of invariants that give an obstruction to the existence of such metrics. Then we show that these invariants can also be written as a product of equivariant classes. From this we give a new, more direct proof of an existing result: the former invariants determining <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mi>Z</mi></math></span><span></span>-stability on a test configuration are equal to the latter invariants related to the existence of <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><mi>Z</mi></math></span><span></span>-critical metrics on the central fibre of the test configuration. This provides a new approach from which to derive the <span><math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"><mi>Z</mi></math></span><span></span>-critical equation.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"302 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140612899","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}
Emilio Franco, Peter B. Gothen, André Oliveira, Ana Peón-Nieto
{"title":"Narasimhan–Ramanan branes and wobbly Higgs bundles","authors":"Emilio Franco, Peter B. Gothen, André Oliveira, Ana Peón-Nieto","doi":"10.1142/s0129167x24410064","DOIUrl":"https://doi.org/10.1142/s0129167x24410064","url":null,"abstract":"<p>Narasimhan–Ramanan branes, introduced by the authors in a previous paper, consist of a family of <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">BBB</mtext></mstyle></math></span><span></span>-branes inside the moduli space of Higgs bundles, and a family of complex Lagrangian subvarieties. It was conjectured that these complex Lagrangian subvarieties support the <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">BBB</mtext></mstyle></math></span><span></span>-branes that are mirror dual to the Narasimhan–Ramanan <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">BBB</mtext></mstyle></math></span><span></span>-branes. In this paper, we show that the support of these branes intersects nontrivially the locus of wobbly Higgs bundles.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"57 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602119","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":"New examples of twisted Brill–Noether loci I","authors":"L. Brambila-Paz, P. E. Newstead","doi":"10.1142/s0129167x24410039","DOIUrl":"https://doi.org/10.1142/s0129167x24410039","url":null,"abstract":"<p>Our purpose in this paper is to construct new examples of twisted Brill–Noether loci on curves of genus <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi><mo>≥</mo><mn>2</mn></math></span><span></span>. Many of these examples have negative expected dimension. We deduce also the existence of a new region in the Brill–Noether map, whose points support non-empty standard Brill–Noether loci.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"95 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601813","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}
Guillermo Gallego, Oscar García-Prada, M. S. Narasimhan
{"title":"Higgs bundles twisted by a vector bundle","authors":"Guillermo Gallego, Oscar García-Prada, M. S. Narasimhan","doi":"10.1142/s0129167x24410076","DOIUrl":"https://doi.org/10.1142/s0129167x24410076","url":null,"abstract":"<p>In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mn>2</mn></math></span><span></span> vector bundle. We define a Hitchin map and give a spectral correspondence. We also state a Hitchin–Kobayashi correspondence for a generalization of Hitchin’s equations to this situation. In a certain sense, this theory lies halfway between the theories of Higgs bundles on a curve and on a higher-dimensional variety.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601737","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}
Indranil Biswas, Sorin Dumitrescu, Lynn Heller, Sebastian Heller, João Pedro dos Santos
{"title":"On the monodromy of holomorphic differential systems","authors":"Indranil Biswas, Sorin Dumitrescu, Lynn Heller, Sebastian Heller, João Pedro dos Santos","doi":"10.1142/s0129167x24410015","DOIUrl":"https://doi.org/10.1142/s0129167x24410015","url":null,"abstract":"<p>First we survey and explain the strategy of some recent results that construct holomorphic <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext>sl</mtext></mstyle><mo stretchy=\"false\">(</mo><mn>2</mn><mo>,</mo><mi>ℂ</mi><mo stretchy=\"false\">)</mo></math></span><span></span>-differential systems over some Riemann surfaces <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi mathvariant=\"normal\">Σ</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span><span></span> of genus <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi><mo>≥</mo><mn>2</mn></math></span><span></span>, satisfying the condition that the image of the associated monodromy homomorphism is (real) Fuchsian [I. Biswas, S. Dumitrescu, L. Heller and S. Heller, Fuchsian sl<span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mn>2</mn><mo>,</mo><mi>ℂ</mi><mo stretchy=\"false\">)</mo></math></span><span></span>-systems of compact Riemann surfaces [with an appendix by Takuro Mochizuki], preprint, arXiv:org/abs/2104.04818] or some cocompact Kleinian subgroup <disp-formula-group><span><math altimg=\"eq-00005.gif\" display=\"block\" overflow=\"scroll\"><mrow><mi mathvariant=\"normal\">Γ</mi><mo>⊂</mo><mstyle><mtext>SL</mtext></mstyle><mo stretchy=\"false\">(</mo><mn>2</mn><mo>,</mo><mi>ℂ</mi><mo stretchy=\"false\">)</mo></mrow></math></span><span></span></disp-formula-group> as in [I. Biswas, S. Dumitrescu, L. Heller and S. Heller, On the existence of holomorphic curves in compact quotients of <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext>SL</mtext></mstyle><mo stretchy=\"false\">(</mo><mn>2</mn><mo>,</mo><mi>ℂ</mi><mo stretchy=\"false\">)</mo></math></span><span></span>, preprint, arXiv:org/abs/2112.03131]. As a consequence, there exist holomorphic maps from <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi mathvariant=\"normal\">Σ</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span><span></span> to the quotient space <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext>SL</mtext></mstyle><mo stretchy=\"false\">(</mo><mn>2</mn><mo>,</mo><mi>ℂ</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">/</mo><mi mathvariant=\"normal\">Γ</mi></math></span><span></span>, where <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"normal\">Γ</mi><mo>⊂</mo><mstyle><mtext>SL</mtext></mstyle><mo stretchy=\"false\">(</mo><mn>2</mn><mo>,</mo><mi>ℂ</mi><mo stretchy=\"false\">)</mo></math></span><span></span> is a cocompact lattice, that do not factor through any elliptic curve [I. Biswas, S. Dumitrescu, L. Heller and S. Heller, On the existence of holomorphic curves in compact quotients of <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext>SL</mtext></mstyle><mo stretchy=\"false\">(</mo><mn>2</mn><mo>,</mo><mi>ℂ</mi><mo stretchy=\"false\">)","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"35 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601814","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":"Simplicity and tracial weights on non-unital reduced crossed products","authors":"Yuhei Suzuki","doi":"10.1142/s0129167x24500216","DOIUrl":"https://doi.org/10.1142/s0129167x24500216","url":null,"abstract":"<p>We extend theorems of Breuillard–Kalantar–Kennedy–Ozawa on unital reduced crossed products to the non-unital case under mild assumptions. As a result simplicity of <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>C</mi></mrow><mrow><mo stretchy=\"false\">∗</mo></mrow></msup></math></span><span></span>-algebras is stable under taking reduced crossed products over discrete <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>C</mi></mrow><mrow><mo stretchy=\"false\">∗</mo></mrow></msup></math></span><span></span>-simple groups, and a similar result for uniqueness of tracial weight. Interestingly, our analysis on tracial weights involves von Neumann algebra theory.</p><p>Our generalizations have two applications. The first is to locally compact groups. We establish stability results of (non-discrete) <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>C</mi></mrow><mrow><mo stretchy=\"false\">∗</mo></mrow></msup></math></span><span></span>-simplicity and the unique trace property under discrete group extensions. The second is to the twisted crossed product. Thanks to the Packer–Raeburn theorem, our results lead to (generalizations of) the results of Bryder–Kennedy by a different method.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"36 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601738","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":"Hitchin map on even very stable upward flows","authors":"Miguel González, Tamás Hausel","doi":"10.1142/s0129167x2441009x","DOIUrl":"https://doi.org/10.1142/s0129167x2441009x","url":null,"abstract":"<p>We define even very stable Higgs bundles and study the Hitchin map restricted to their upward flows. In the <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mstyle><mtext mathvariant=\"normal\">GL</mtext></mstyle></mrow><mrow><mi>n</mi></mrow></msub></math></span><span></span> case, we classify the type <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mn>1</mn><mo stretchy=\"false\">)</mo></math></span><span></span> examples, and find that they are governed by a root system formed by the roots of even height. We discuss how the spectrum of equivariant cohomology of real and quaternionic Grassmannians, <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mn>4</mn><mi>n</mi></math></span><span></span>-spheres and the real Cayley plane appear to describe the Hitchin map on even cominuscule upward flows. The even upward flows in question are the same as upward flows in Higgs bundle moduli spaces for quasi-split inner real forms. The latter spaces have been pioneered by Oscar García-Prada and his collaborators.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"85 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601872","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":"Framed parabolic sheaves on a trinion","authors":"Indranil Biswas, Jacques Hurtubise","doi":"10.1142/s0129167x24410027","DOIUrl":"https://doi.org/10.1142/s0129167x24410027","url":null,"abstract":"<p>We consider for structure groups <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">SU</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>n</mi><mo stretchy=\"false\">)</mo><mspace width=\".17em\"></mspace><mo>⊂</mo><mspace width=\".17em\"></mspace><mstyle><mtext mathvariant=\"normal\">SL</mtext></mstyle><mo stretchy=\"false\">(</mo><mi>n</mi><mo>,</mo><mi>ℂ</mi><mo stretchy=\"false\">)</mo></math></span><span></span> a densely defined toric structure on the moduli space of framed parabolic sheaves on a three-punctured sphere, which degenerates to an actual toric structure. In combination with previous degeneration results, these extend to similar moduli for arbitrary Riemann surfaces.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":"100 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601913","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}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
