Asian Journal of Mathematics

Volume 26 (2022)

Number 4

Invariance of plurigenera and Chow-type lemma

Pages: 507 – 554

DOI: https://dx.doi.org/10.4310/AJM.2022.v26.n4.a2

Authors

Sheng Rao (School of Mathematics and Statistics, Wuhan University, Wuhan, China; and Université de Grenoble-Alpes, Institut Fourier (Mathématiques) UMR 5582 du C.N.R.S., Gières, France)

I-Hsun Tsai (Department of Mathematics, National Taiwan University, Taipei, Taiwan)

Abstract

This paper answers a question of Demailly whether a smooth family of nonsingular projective varieties admits the deformation invariance of plurigenera affirmatively, and proves this more generally for a flat family of varieties with only canonical singularities and uncountable ones therein being of general type and also two Chow-type lemmata on the structure of a family of projective complex analytic spaces.

Keywords

deformations of complex structures, modifications, resolution of singularities, spectral sequences, hypercohomology, analytic sheaves and cohomology groups

2010 Mathematics Subject Classification

Primary 32G05. Secondary 18G40, 32C35, 32S45.

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In Memory of Jean-Pierre Demailly (1957–2022)

Rao is partially supported by NSFC (Grant No. 11671305, 11771339, 11922115) and the Fundamental Research Funds for the Central Universities (Grant No. 2042020kf1065).

Received 1 June 2022

Accepted 15 June 2022

Published 24 March 2023