Hacon generic vanishing
WebDec 1, 2024 · This is the first blog aim to introduce the generic vanishing theorem, follows Hacon’s proof. He use the Fourier-Mukai transform and something about Abelian … Web4 BHARGAV BHATT Thus, any abstract statement that is true for all groups will also be true for all group schemes (e.g. it su ces to check compatibility with multiplication when showing that a morphism of schemes is a homomorphism of group
Hacon generic vanishing
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WebJan 5, 2015 · The aim of this paper is to present an approach to Green–Lazarsfeld'sgeneric vanishing combining Gaussian maps and the Fourier–Mukai transform associated with the Poincaré line bundle. As an application, we prove the generic vanishing theorem for all normal Cohen–Macaulay subvarieties of abelian varieties over an algebraically closed field. WebAug 29, 2016 · As a corollary, we recover a result of Hacon and Kovács, producing counterexamples to Generic Vanishing in dimension 3 and higher. Comments: 12 …
WebHacon’s proof of generic vanishing theorems via Fourier– Mukai transforms for abelian varieties. References: A derived category approach to generic vanishing, J. Reine Angew. Math. 575 (2004), 173–187. Su Xiaoyu. Mar 09. Original proof of the generic vanishing … WebChristopher D. Hacon Born: February 14, 1970, Manchester England Nationality: English, Italian and USA. Address: Department of Mathematics, University of Utah ... [58] Generic vanishing in characteristic p>0 and the characteriza-tion of ordinary abelian varieties (with Z. Patakfalvi. arXiv:1310.2996 Amer. Jour. Math. Math. Volume 138, Number 4 ...
Webspectacular developments. Ein and Lazarsfeld, using generic vanishing theorems of Green and Lazarsfeld, proved in [EL] that irreducible theta divisors are normal and gave an optimal bound on the dimension of the locus of points of given multiplicity of a multitheta divisor. Hacon de-termined in [H1] exactly when this bound is attained and ... Web2 CHRISTOPHER D. HACON AND SANDOR J KOV´ ACS´ ... (1.3) may be interpreted as saying that generic vanishing does not extended to singular varieties in a non-trivial …
WebOct 11, 2013 · We prove a generic vanishing type statement in positive characteristic and apply it to prove positive characteristic versions of Kawamata's theorems: a …
WebThe term “generic vanishing” refers to a collection of theorems about the coho-mology of line bundles with trivial first Chern class. The first results of this type were obtained by Green and Lazarsfeld in the late 1980s [GL87, GL91]; they were ... Hacon [Hac04, §4] showed that if f: X → A is a morphism from a smooth pro- ... redefinir adaptador ethernetWebSTRONG GENERIC VANISHING AND A HIGHER DIMENSIONAL CASTELNUOVO-DE FRANCHIS INEQUALITY GIUSEPPE PARESCHI AND MIHNEA POPA 1. Introduction ... work of Hacon-Pardini on the classi cation of certain irregular varieties. The case ˜(! X) = 1 is worked out in [HP3], while some of its consequences already appeared in [HP2], both … kochclub hamburg campingweckenWebCourse Description In these lectures we will survey the generic vanishing results of Green, Lazarfeld, Hacon, Popa, Pareschi and others and discuss their applications to the study … redefinir facebookWebOur main tools are the generic vanishing the-orems of Green and Lazarsfeld and the characterization of theta divisors given by Hacon in Corollary 3.4 of Fourier transforms, generic vanishing theorems and polarizations of abelian varieties. 1. INTRODUCTION The purpose of this paper is to show how the generic vanishing theorems of redefinir browserWebGeneric vanishing fails for singular varieties and in characteristic p>0 Christopher D. Hacon and Sándor J. Kovács 14. Deformations of elliptic Calabi–Yau manifolds János Kollár ... Christopher D. Hacon, University of Utah Christopher D. Hacon is a distinguished professor at the University of Utah. He is a recipient of the 2007 Clay ... kochbuch coming homeredefinir appleWebHacon’s generic vanishing theorem for higher direct images of canonical sheaves, which is already one of the most relevant applications of the Fourier–Mukai methods in the present context. The last three sections are devoted respectively to the work of Ein and Lazarsfeld, to the Chen–Hacon characterization of abelian ... kochbuch the taste 2022