Pub Date : 2022-01-01Epub Date: 2022-10-19DOI: 10.1007/s00032-022-00369-8
M Varesco, C Voisin
We first describe the construction of the Kuga-Satake variety associated to a (polarized) weight-two Hodge structure of hyper-Kähler type. We describe the classical cases where the Kuga-Satake correspondence between a hyper-Kähler manifold and its Kuga-Satake variety has been proved to be algebraic. We then turn to recent work of O'Grady and Markman which we combine to prove that the Kuga-Satake correspondence is algebraic for projective hyper-Kähler manifolds of generalized Kummer deformation type.
{"title":"Hyper-Kähler Manifolds of Generalized Kummer Type and the Kuga-Satake Correspondence.","authors":"M Varesco, C Voisin","doi":"10.1007/s00032-022-00369-8","DOIUrl":"https://doi.org/10.1007/s00032-022-00369-8","url":null,"abstract":"<p><p>We first describe the construction of the Kuga-Satake variety associated to a (polarized) weight-two Hodge structure of hyper-Kähler type. We describe the classical cases where the Kuga-Satake correspondence between a hyper-Kähler manifold and its Kuga-Satake variety has been proved to be algebraic. We then turn to recent work of O'Grady and Markman which we combine to prove that the Kuga-Satake correspondence is algebraic for projective hyper-Kähler manifolds of generalized Kummer deformation type.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"90 2","pages":"433-444"},"PeriodicalIF":1.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9708794/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35254892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01Epub Date: 2022-03-24DOI: 10.1007/s00032-022-00350-5
Manuel Friedrich, Manuel Seitz, Ulisse Stefanelli
Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual orientations of the squares and that these patterns are periodic and one-dimensional. In contrast to the flat case, the nonflatness of the tiles gives rise to nontrivial geometries, with configurations bending, wrinkling, or even rolling up in one direction.
{"title":"Tilings with Nonflat Squares: A Characterization.","authors":"Manuel Friedrich, Manuel Seitz, Ulisse Stefanelli","doi":"10.1007/s00032-022-00350-5","DOIUrl":"10.1007/s00032-022-00350-5","url":null,"abstract":"<p><p>Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual orientations of the squares and that these patterns are periodic and one-dimensional. In contrast to the flat case, the nonflatness of the tiles gives rise to nontrivial geometries, with configurations bending, wrinkling, or even rolling up in one direction.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"90 1","pages":"131-175"},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9242529/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40468789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01Epub Date: 2022-10-03DOI: 10.1007/s00032-022-00364-z
Alessio Bottini
In these notes we review some basic facts about the LLV Lie algebra. It is a rational Lie algebra, introduced by Looijenga-Lunts and Verbitsky, acting on the rational cohomology of a compact Kähler manifold. We study its structure and describe one irreducible component of the rational cohomology in the case of a compact hyperkähler manifold.
{"title":"The Looijenga-Lunts-Verbitsky Algebra and Verbitsky's Theorem.","authors":"Alessio Bottini","doi":"10.1007/s00032-022-00364-z","DOIUrl":"10.1007/s00032-022-00364-z","url":null,"abstract":"<p><p>In these notes we review some basic facts about the LLV Lie algebra. It is a rational Lie algebra, introduced by Looijenga-Lunts and Verbitsky, acting on the rational cohomology of a compact Kähler manifold. We study its structure and describe one irreducible component of the rational cohomology in the case of a compact hyperkähler manifold.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"90 2","pages":"403-416"},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9708818/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35254894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01Epub Date: 2022-03-19DOI: 10.1007/s00032-022-00349-y
D Huybrechts, M Mauri
We review the theory of Lagrangian fibrations of hyperkähler manifolds as initiated by Matsushita. We also discuss more recent work of Shen-Yin and Harder-Li-Shen-Yin. Occasionally, we give alternative arguments and complement the discussion by additional observations.
{"title":"Lagrangian Fibrations.","authors":"D Huybrechts, M Mauri","doi":"10.1007/s00032-022-00349-y","DOIUrl":"https://doi.org/10.1007/s00032-022-00349-y","url":null,"abstract":"<p><p>We review the theory of Lagrangian fibrations of hyperkähler manifolds as initiated by Matsushita. We also discuss more recent work of Shen-Yin and Harder-Li-Shen-Yin. Occasionally, we give alternative arguments and complement the discussion by additional observations.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"90 2","pages":"459-483"},"PeriodicalIF":1.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9708819/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35254893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-01DOI: 10.1007/s00032-021-00340-z
C. O. Alves, V. Ambrosio, C. Ledesma
{"title":"An Existence Result for a Class of Magnetic Problems in Exterior Domains","authors":"C. O. Alves, V. Ambrosio, C. Ledesma","doi":"10.1007/s00032-021-00340-z","DOIUrl":"https://doi.org/10.1007/s00032-021-00340-z","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"89 1","pages":"523 - 550"},"PeriodicalIF":1.7,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43894024","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}
Pub Date : 2021-11-16DOI: 10.1007/s00032-021-00345-8
G. Moscariello, Giulio Pascale
{"title":"Second Order Regularity for a Linear Elliptic System Having BMO Coefficients","authors":"G. Moscariello, Giulio Pascale","doi":"10.1007/s00032-021-00345-8","DOIUrl":"https://doi.org/10.1007/s00032-021-00345-8","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"89 1","pages":"413 - 432"},"PeriodicalIF":1.7,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47549578","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}
Pub Date : 2021-08-04DOI: 10.1007/s00032-022-00353-2
F. F. Favale, G. Pirola
{"title":"Infinitesimal Variation Functions for Families of Smooth Varieties","authors":"F. F. Favale, G. Pirola","doi":"10.1007/s00032-022-00353-2","DOIUrl":"https://doi.org/10.1007/s00032-022-00353-2","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"90 1","pages":"209 - 228"},"PeriodicalIF":1.7,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48727319","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}
Pub Date : 2021-08-02DOI: 10.1007/s00032-021-00342-x
D. Serre
{"title":"Projective Properties of Divergence-Free Symmetric Tensors, and New Dispersive Estimates in Gas Dynamics","authors":"D. Serre","doi":"10.1007/s00032-021-00342-x","DOIUrl":"https://doi.org/10.1007/s00032-021-00342-x","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"89 1","pages":"433 - 452"},"PeriodicalIF":1.7,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45119442","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}
Pub Date : 2021-07-17DOI: 10.1007/s00032-021-00341-y
J. Dolbeault
{"title":"Functional Inequalities: Nonlinear Flows and Entropy Methods as a Tool for Obtaining Sharp and Constructive Results","authors":"J. Dolbeault","doi":"10.1007/s00032-021-00341-y","DOIUrl":"https://doi.org/10.1007/s00032-021-00341-y","url":null,"abstract":"","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"89 1","pages":"355 - 386"},"PeriodicalIF":1.7,"publicationDate":"2021-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43578111","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}
Pub Date : 2021-06-08DOI: 10.1007/s00032-021-00332-z
Massimo Bertolini, Marco Adamo Seveso, Rodolfo Venerucci
This article proves a case of the p-adic Birch and Swinnerton–Dyer conjecture for Garrett p-adic L-functions of (Bertolini et al. in On p-adic analogues of the Birch and Swinnerton–Dyer conjecture for Garrett L-functions, 2021), in the imaginary dihedral exceptional zero setting of extended analytic rank 4.
本文证明了在扩展解析秩4的虚二面体例外零设置中(Bertolini et al. On On Birch和Swinnerton-Dyer猜想的Garrett l函数的p进Birch和Swinnerton-Dyer猜想，2021)的Garrett p进l函数的p进Birch和Swinnerton-Dyer猜想的一个例子。
{"title":"Heegner Points and Exceptional Zeros of Garrett p-Adic L-Functions","authors":"Massimo Bertolini, Marco Adamo Seveso, Rodolfo Venerucci","doi":"10.1007/s00032-021-00332-z","DOIUrl":"https://doi.org/10.1007/s00032-021-00332-z","url":null,"abstract":"<p>This article proves a case of the <i>p</i>-adic Birch and Swinnerton–Dyer conjecture for Garrett <i>p</i>-adic <i>L</i>-functions of (Bertolini et al. in On <i>p</i>-adic analogues of the Birch and Swinnerton–Dyer conjecture for Garrett <i>L</i>-functions, 2021), in the imaginary dihedral exceptional zero setting of extended analytic rank 4.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"3 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516917","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}
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