Universität zu Köln

Hsiao, Chin-Yu and Marinescu, George ORCID: 0000-0001-6539-7860 (2017). Berezin-Toeplitz quantization for lower energy forms. Commun. Partial Differ. Equ., 42 (6). S. 895 - 943. PHILADELPHIA: TAYLOR & FRANCIS INC. ISSN 1532-4133

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Abstract

Let M be an arbitrary complex manifold and let L be a Hermitian holomorphic line bundle over M. We introduce the Berezin-Toeplitz quantization of the open set of M where the curvature on L is nondegenerate. In particular, we quantize any manifold admitting a positive line bundle. The quantum spaces are the spectral spaces corresponding to [0,k(-N)], where N>1 is fixed, of the Kodaira Laplace operator acting on forms with values in tensor powers L-k. We establish the asymptotic expansion of associated Toeplitz operators and their composition in the semiclassical limit k and we define the corresponding star-product. If the Kodaira Laplace operator has a certain spectral gap this method yields quantization by means of harmonic forms. As applications, we obtain the Berezin-Toeplitz quantization for semi-positive and big line bundles.

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:38-245825
DOI:	10.1080/03605302.2017.1330340
Journal or Publication Title:	Commun. Partial Differ. Equ.
Volume:	42
Number:	6
Page Range:	S. 895 - 943
Date:	2017
Publisher:	TAYLOR & FRANCIS INC
Place of Publication:	PHILADELPHIA
ISSN:	1532-4133
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 ASYMPTOTIC-EXPANSION; MORSE INEQUALITIES; KAHLER-MANIFOLDS; BERGMAN-KERNEL; DEFORMATION; OPERATORS Multiple languages Mathematics, Applied; Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/24582