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Quartic surfaces up to volume preserving equivalence 四次曲面直至保持体积等值
2区 数学
Selecta Mathematica-New Series Pub Date : 2023-11-14 DOI: 10.1007/s00029-023-00890-7
Tom Ducat
{"title":"Quartic surfaces up to volume preserving equivalence","authors":"Tom Ducat","doi":"10.1007/s00029-023-00890-7","DOIUrl":"https://doi.org/10.1007/s00029-023-00890-7","url":null,"abstract":"Abstract We study log Calabi–Yau pairs of the form $$(mathbb {P}^3,Delta )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>,</mml:mo> <mml:mi>Δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , where $$Delta $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Δ</mml:mi> </mml:math> is a quartic surface, and classify all such pairs of coregularity less than or equal to one, up to volume preserving equivalence. In particular, if $$(mathbb {P}^3,Delta )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>,</mml:mo> <mml:mi>Δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is a maximal log Calabi–Yau pair then we show that it has a toric model.","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134901344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Wronskians, total positivity, and real Schubert calculus 朗斯基式，全正性，和实舒伯特微积分
2区 数学
Selecta Mathematica-New Series Pub Date : 2023-11-13 DOI: 10.1007/s00029-023-00888-1
Steven N. Karp
{"title":"Wronskians, total positivity, and real Schubert calculus","authors":"Steven N. Karp","doi":"10.1007/s00029-023-00888-1","DOIUrl":"https://doi.org/10.1007/s00029-023-00888-1","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134993022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Exact uniform approximation and Dirichlet spectrum in dimension at least two 精确均匀近似和至少二维的狄利克雷谱
2区 数学
Selecta Mathematica-New Series Pub Date : 2023-11-01 DOI: 10.1007/s00029-023-00889-0
Johannes Schleischitz
{"title":"Exact uniform approximation and Dirichlet spectrum in dimension at least two","authors":"Johannes Schleischitz","doi":"10.1007/s00029-023-00889-0","DOIUrl":"https://doi.org/10.1007/s00029-023-00889-0","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135371434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
The partial compactification of the universal centralizer 万能扶正器的部分紧实性
2区 数学
Selecta Mathematica-New Series Pub Date : 2023-10-27 DOI: 10.1007/s00029-023-00873-8
Ana Bălibanu
{"title":"The partial compactification of the universal centralizer","authors":"Ana Bălibanu","doi":"10.1007/s00029-023-00873-8","DOIUrl":"https://doi.org/10.1007/s00029-023-00873-8","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136234566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
A generalization of cyclic shift classes 循环移位类的推广
2区 数学
Selecta Mathematica-New Series Pub Date : 2023-10-26 DOI: 10.1007/s00029-023-00885-4
Xuhua He
{"title":"A generalization of cyclic shift classes","authors":"Xuhua He","doi":"10.1007/s00029-023-00885-4","DOIUrl":"https://doi.org/10.1007/s00029-023-00885-4","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134909989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Instanton homology and knot detection on thickened surfaces 加厚表面上的瞬子同源性和结检测
2区 数学
Selecta Mathematica-New Series Pub Date : 2023-10-26 DOI: 10.1007/s00029-023-00884-5
Zhenkun Li, Yi Xie, Boyu Zhang
{"title":"Instanton homology and knot detection on thickened surfaces","authors":"Zhenkun Li, Yi Xie, Boyu Zhang","doi":"10.1007/s00029-023-00884-5","DOIUrl":"https://doi.org/10.1007/s00029-023-00884-5","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136376344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Homotopy cardinality via extrapolation of Morava–Euler characteristics 基于Morava-Euler特征外推的同伦基数
2区 数学
Selecta Mathematica-New Series Pub Date : 2023-10-26 DOI: 10.1007/s00029-023-00886-3
Lior Yanovski
{"title":"Homotopy cardinality via extrapolation of Morava–Euler characteristics","authors":"Lior Yanovski","doi":"10.1007/s00029-023-00886-3","DOIUrl":"https://doi.org/10.1007/s00029-023-00886-3","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136381574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Zoo of monotone Lagrangians in $${mathbb {C}}P^n$$ $${mathbb {C}}P^n$ 中的单调拉格朗日动物园
2区 数学
Selecta Mathematica-New Series Pub Date : 2023-10-26 DOI: 10.1007/s00029-023-00881-8
Vardan Oganesyan
{"title":"Zoo of monotone Lagrangians in $${mathbb {C}}P^n$$","authors":"Vardan Oganesyan","doi":"10.1007/s00029-023-00881-8","DOIUrl":"https://doi.org/10.1007/s00029-023-00881-8","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136377024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess–Zumino–Witten fusion rings 椭圆rujsenaars差分算子，对称多项式和Wess-Zumino-Witten融合环
2区 数学
Selecta Mathematica-New Series Pub Date : 2023-10-25 DOI: 10.1007/s00029-023-00883-6
van Diejen, Jan Felipe, Görbe, Tamás
{"title":"Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess–Zumino–Witten fusion rings","authors":"van Diejen, Jan Felipe, Görbe, Tamás","doi":"10.1007/s00029-023-00883-6","DOIUrl":"https://doi.org/10.1007/s00029-023-00883-6","url":null,"abstract":"The fusion ring for $widehat{mathfrak{su}}(n)_m$ Wess-Zumino-Witten conformal field theories is known to be isomorphic to a factor ring of the ring of symmetric polynomials presented by Schur polynomials. We introduce a deformation of this factor ring associated with eigenpolynomials for the elliptic Ruijsenaars difference operators. The corresponding Littlewood-Richardson coefficients are governed by a Pieri rule stemming from the eigenvalue equation. The orthogonality of the eigenbasis gives rise to an analog of the Verlinde formula. In the trigonometric limit, our construction recovers the refined $widehat{mathfrak{su}}(n)_m$ Wess-Zumino-Witten fusion ring associated with the Macdonald polynomials.","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134972236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Computational aspects of Calogero–Moser spaces Calogero-Moser空间的计算方面
2区 数学
Selecta Mathematica-New Series Pub Date : 2023-10-24 DOI: 10.1007/s00029-023-00878-3
Cédric Bonnafé, Ulrich Thiel
{"title":"Computational aspects of Calogero–Moser spaces","authors":"Cédric Bonnafé, Ulrich Thiel","doi":"10.1007/s00029-023-00878-3","DOIUrl":"https://doi.org/10.1007/s00029-023-00878-3","url":null,"abstract":"Abstract We present a series of algorithms for computing geometric and representation-theoretic invariants of Calogero–Moser spaces and rational Cherednik algebras associated with complex reflection groups. In particular, we are concerned with Calogero–Moser families (which correspond to the $$mathbb {C}^times $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mo>×</mml:mo> </mml:msup> </mml:math> -fixed points of the Calogero–Moser space) and cellular characters (a proposed generalization by Rouquier and the first author of Lusztig’s constructible characters based on a Galois covering of the Calogero–Moser space). To compute the former, we devised an algorithm for determining generators of the center of the rational Cherednik algebra (this algorithm has several further applications), and to compute the latter we developed an algorithmic approach to the construction of cellular characters via Gaudin operators. We have implemented all our algorithms in the Cherednik Algebra Magma Package by the second author and used this to confirm open conjectures in several new cases. As an interesting application in birational geometry we are able to determine for many exceptional complex reflection groups the chamber decomposition of the movable cone of a $$mathbb {Q}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Q</mml:mi> </mml:math> -factorial terminalization (and thus the number of non-isomorphic relative minimal models) of the associated symplectic singularity. Making possible these computations was also a source of inspiration for the first author to propose several conjectures about the geometry of Calogero–Moser spaces (cohomology, fixed points, symplectic leaves), often in relation with the representation theory of finite reductive groups.","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135220364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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