On Kollár's vanishing theorems. I
type: Item
instance of: scholarly article
title: On Kollár's vanishing theorems. I
zbMATH Open document ID: 0715.14008
DOI: 10.1215/S0012-7094-89-05923-1
author: Jerome William Hoffman
published in: Duke Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: Let \(\pi\) : \(X\to Y\) be a smooth morphism of projective nonsingular varieties. One gives a vanishing theorem involving certain complexes of sheaves on Y which appear in the construction by Deligne and Zucker of Hodge structures on the Leray factors \(H^ s(Y,R^ t\pi_*{\mathbb{C}})\). In fact the theorem concerns an arbitrary variation of Hodge structures over Y. The results extend Kollár's (and Kodaira's) vanishing theorem.
reviewed by: Nicolae Manolache
Mathematics Subject Classification ID: 14F17
Mathematics Subject Classification ID: 14D07
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 4177248
zbMATH Keywords: variation of Hodge structures
zbMATH Keywords: vanishing theorem
MaRDI profile type: Publication
cites work: Introduction to Grothendieck duality theory
cites work: A note on Kollár's theorem
cites work: Q5589101
cites work: \(L^ 2\) and intersection cohomologies for a polarizable variation of Hodge structure
cites work: Equations différentielles à points singuliers réguliers
cites work: Théoreme de Lefschetz et critères de dégénérescence de suites spectrales
cites work: Théorie de Hodge. II. (Hodge theory. II)
cites work: Théorie de Hodge. III
cites work: Q3791256
cites work: Logarithmic de Rham complexes and vanishing theorems
cites work: Periods of integrals on algebraic manifolds: Summary of main results and discussion of open problems
cites work: Periods of integrals on algebraic manifolds. III: Some global differential-geometric properties of the period mapping
cites work: Q4126449
cites work: Q5596003
cites work: Q4143433
cites work: Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
cites work: Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin
cites work: On the differentiation of De Rham cohomology classes with respect to parameters
cites work: On a Differential-Geometric Method in the Theory of Analytic Stacks
cites work: On a Theorem of Lefschetz and the Lemma of Enriques-Severi-Zariski
cites work: Higher direct images of dualizing sheaves. I
cites work: Higher direct images of dualizing sheaves. II
cites work: Q4089110
cites work: On complex analytic vector bundles
cites work: Hodge filtrations and the higher direct images of canonical sheaves
cites work: Q4402617
cites work: Q3705705
cites work: Hodge theory with degenerating coefficients: \(L_2\) cohomology in the Poincaré metric
Recommended article: A Kollár-type vanishing theorem
Recommended article: A vanishing theorem of Kollár-Ohsawa type
Recommended article: A remark on Kovács's vanishing theorem
Recommended article: Kollár-Nadel type vanishing theorem
Recommended article: Vanishing theorems on complete Kähler manifolds
Recommended article: Vanishing theorems on complete Kähler manifolds and their applications
Recommended article: Q4954717
Recommended article: A Kawamata-Viehweg vanishing theorem on compact Kähler manifolds.
Recommended article: Kählerian versions of the vanishing theorem of Bogomolov
Recommended article: A vanishing theorem ``à la Kawamata-Viehweg''
description: scientific article; zbMATH DE number 4177248