Universität zu Köln

Hsiao, Chin-Yu and Marinescu, George ORCID: 0000-0001-6539-7860 (2014). Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles. Commun. Anal. Geom., 22 (1). S. 1 - 109. SOMERVILLE: INT PRESS BOSTON, INC. ISSN 1944-9992

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Abstract

In this paper we study the asymptotic behaviour of the spectral function corresponding to the lower part of the spectrum of the Kodaira Laplacian on high tensor powers of a holomorphic line bundle. This implies a full asymptotic expansion of this function on the set where the curvature of the line bundle is non-degenerate. As application we obtain the Bergman kernel asymptotics for adjoint semi-positive line bundles over complete Kahler manifolds, on the set where the curvature is positive. We also prove the asymptotics for big line bundles endowed with singular Hermitian metrics with strictly positive curvature current. In this case, the full asymptotics holds outside the singular locus of the metric.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Hsiao, Chin-Yu UNSPECIFIED UNSPECIFIED UNSPECIFIED Marinescu, George UNSPECIFIED orcid.org/0000-0001-6539-7860 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-450453
Journal or Publication Title:	Commun. Anal. Geom.
Volume:	22
Number:	1
Page Range:	S. 1 - 109
Date:	2014
Publisher:	INT PRESS BOSTON, INC
Place of Publication:	SOMERVILLE
ISSN:	1944-9992
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MORSE INEQUALITIES; TOEPLITZ QUANTIZATION; VECTOR-BUNDLES; EXPANSION; METRICS; SECTIONS; THEOREM Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/45045