Hacon generic vanishing

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August undefined, 2024

WebOct 11, 2013 · Generic vanishing in characteristic p > 0 and the characterization of ordinary abelian varieties @article{Hacon2013GenericVI, title={Generic vanishing in characteristic p > 0 and the characterization of ordinary abelian varieties}, author={Christopher D. Hacon and Zsolt Patakfalvi}, journal={American Journal of …

Generic Vanishing Fails for Surfaces in Positive Characteristic

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 … WebThe term \generic vanishing" refers to a collection of theorems about the coho-mology of line bundles with trivial rst Chern class. The rst results of this type ... Hacon [Hac04, x4] showed that if f: X!Ais a morphism from a smooth pro-jective variety to an abelian variety, then the higher direct image sheaves Rjf! X tankless water heater boston

[math/0308198] A derived category approach to generic vanishing

WebOur 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 http://library.msri.org/books/Book59/files/67pare.pdf WebHacon’s proof using the Fourier-Mukai transform and some results of mixed Hodge theory (Kollar’s vanishing theorem) and we left this as a blackbox. Actually the most important … tankless water heater breaker requirements

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GenericVanishingFailsforSurfacesinPositive Characteristic - arXiv

WebVanishing Theorems The generic vanishing theorem of Green and Lazarsfeld The Fourier Mukai transform A derived category approach to Generic Vanishing Pluricanonical ... Weband Lazarsfeld, using generic vanishing theorems of Green and Lazarsfeld, proved in [3] 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 determined in [5] exactly when this bound is attained and obtained in [6] results tankless water heater boiler combinationWebTHE GENERIC VANISHING THEOREM WENQI LI Abstract. The generic vanishing theorem asserts that general topologically trivial line bundles on a compact K¨ahler … tankless water heater brand recommendation

"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. " - Hacon generic vanishing

Hacon generic vanishing

[PDF] Generic vanishing in characteristic p > 0 and the ...

WebCourse 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 of the birational geometry of irregular varieties i.e. smooth projective varieties such that \(H^0(\Omega^1_X) \neq 0 \). WebApr 5, 2024 · In a recent paper, Hacon and Kovács show that Generic Vanishing does not extend to singular varieties, nor to positive characteristic . As for the positive …

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WebChristopher Hacon On Generic vanishing in char p > 0. Generic fails vanishing in char. p > 0 If char >0, then there are examples of Z a smooth 6-fold and L a very ample line … WebHacon’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 ...

Webby Green and Lazarsfeld (and further sharpened by Chen, Hacon, Pareschi, Popa, Schnell, Simpson and others). On the other hand, in positive characteristic very little is known about generic vanishing and m.A.d. varieties. By a result of the first ... GENERIC VANISHING AND ORDINARY ABELIAN VARIETIES 965 the vanishing Hi(Râ(DA{Rja*ujx))) = 0 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 pages, Bollettino dell'Unione Matematica Italiana (2024)

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 … WebSep 5, 2024 · In this paper, we prove a strengthening of the generic vanishing result in characteristic \(p>0\) given in Hacon and Patakfalvi (Am J Math 138(4):963–998, 2016).

WebAug 20, 2003 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

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 … tankless water heater btu usageWebDec 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 … tankless water heater brands electricWeb4 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 tankless water heater boilerWebIn this paper, we prove a strengthening of the generic vanishing result in characteristic \(p>0\) given in Hacon and Patakfalvi (Am J Math 138(4):963–998, 2016). tankless water heater breaker sizeWebSuper Global Course Special Lectures (Algebraic Geometry)"Generic vanishing and the birational geometry of irregular varieties" Lecture 1Christopher HaconKyo... tankless water heater burning elementsWebMay 4, 2015 · We extend the results of generic vanishing theory to polarizable real Hodge modules on compact complex tori, and from there to arbitrary compact Kahler manifolds. As applications, we obtain a bimeromorphic characterization of compact complex tori among compact Kahler manifolds, semi-positivity results, and a description of the Leray filtration … tankless water heater burner unitWebWe show that there exist smooth surfaces violating Generic Vanishing in any characteristic p ≥ 3. As a corollary, we recover a result of Hacon and Kov´acs, producing … tankless water heater btu