Infinitesimal Torelli theorem for complete intersections in certain homogeneous Kähler manifolds
type: Item
instance of: scholarly article
title: Infinitesimal Torelli theorem for complete intersections in certain homogeneous Kähler manifolds
zbMATH Open document ID: 0627.14009
author: Kazuhiro Konno
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1986-01-01T00:00:00Z
review text: The result proved in this paper is a generalization of the theorem of Peters and Usui that the infinitesimal Torelli theorem holds for any nonsingular complete intersection with ample canonical bundle in a projective space. Let Y be a compact, simply-connected, homogeneous Kähler manifold whose second Betti number is one. The author shows that if X is a nonsingular complete intersection in Y with ample canonical bundle then the infinitesimal Torelli theorem holds for X, provided that at least one of several conditions on X and Y is satisfied. For example, it is enough to assume that Y is an irreducible Hermitian symmetric space of compact type. It is hoped that the proof can be modified to apply when these conditions are omitted.
Mathematics Subject Classification ID: 14C99
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 32M10
zbMATH DE Number: 4019206
zbMATH Keywords: infinitesimal Torelli theorem
zbMATH Keywords: complete intersection
reviewed by: Frances Kirwan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228413
OpenAlex ID: W4244743673
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DOI: 10.2748/TMJ/1178228413
description: scientific article; zbMATH DE number 4019206