SINGULAR HOLOMORPHIC MORSE INEQUALITIES ON NON-COMPACT MANIFOLDS

Dan Coman; George Marinescu; Huan Wang

doi:10.59277/RRMPA.2023.61.82

SINGULAR HOLOMORPHIC MORSE INEQUALITIES ON NON-COMPACT MANIFOLDS

Dan Coman, George Marinescu, Huan Wang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We obtain asymptotic estimates of the dimension of cohomology on possibly non-compact complex manifolds for line bundles endowed with Hermitian metrics with algebraic singularities. We give a unified approach to establishing singular holomorphic Morse inequalities for hyperconcave manifolds, pseudoconvex domains, q-convex manifolds and q-concave manifolds, and we generalize related estimates of Berndtsson. We also consider the case of metrics with more general than algebraic singularities.

Original language	English (US)
Pages (from-to)	61-82
Number of pages	22
Journal	REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES
Volume	68
Issue number	1-2
DOIs	https://doi.org/10.59277/RRMPA.2023.61.82
State	Published - 2023

Keywords

holomorphic Morse inequalities
hyperconcave
pseudoconvex domain
q-concave manifold
q-convex
singular Hermitian metric of a line bundle

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.59277/RRMPA.2023.61.82

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title = "SINGULAR HOLOMORPHIC MORSE INEQUALITIES ON NON-COMPACT MANIFOLDS",

abstract = "We obtain asymptotic estimates of the dimension of cohomology on possibly non-compact complex manifolds for line bundles endowed with Hermitian metrics with algebraic singularities. We give a unified approach to establishing singular holomorphic Morse inequalities for hyperconcave manifolds, pseudoconvex domains, q-convex manifolds and q-concave manifolds, and we generalize related estimates of Berndtsson. We also consider the case of metrics with more general than algebraic singularities.",

keywords = "holomorphic Morse inequalities, hyperconcave, pseudoconvex domain, q-concave manifold, q-convex, singular Hermitian metric of a line bundle",

author = "Dan Coman and George Marinescu and Huan Wang",

year = "2023",

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T1 - SINGULAR HOLOMORPHIC MORSE INEQUALITIES ON NON-COMPACT MANIFOLDS

AU - Coman, Dan

AU - Marinescu, George

AU - Wang, Huan

PY - 2023

Y1 - 2023

N2 - We obtain asymptotic estimates of the dimension of cohomology on possibly non-compact complex manifolds for line bundles endowed with Hermitian metrics with algebraic singularities. We give a unified approach to establishing singular holomorphic Morse inequalities for hyperconcave manifolds, pseudoconvex domains, q-convex manifolds and q-concave manifolds, and we generalize related estimates of Berndtsson. We also consider the case of metrics with more general than algebraic singularities.

AB - We obtain asymptotic estimates of the dimension of cohomology on possibly non-compact complex manifolds for line bundles endowed with Hermitian metrics with algebraic singularities. We give a unified approach to establishing singular holomorphic Morse inequalities for hyperconcave manifolds, pseudoconvex domains, q-convex manifolds and q-concave manifolds, and we generalize related estimates of Berndtsson. We also consider the case of metrics with more general than algebraic singularities.

KW - holomorphic Morse inequalities

KW - hyperconcave

KW - pseudoconvex domain

KW - q-concave manifold

KW - q-convex

KW - singular Hermitian metric of a line bundle

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JO - REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES

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ER -

SINGULAR HOLOMORPHIC MORSE INEQUALITIES ON NON-COMPACT MANIFOLDS

Abstract

Keywords

ASJC Scopus subject areas

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