Global 2-forms on regular 3-folds of general type
type: Item
instance of: scholarly article
title: Global 2-forms on regular 3-folds of general type
zbMATH Open document ID: 0838.14032
DOI: 10.1215/S0012-7094-93-07132-3
author: Tie Luo
published in: Duke Mathematical Journal
publication date: 1994-06-05T00:00:00Z
review text: Let \(V\) be a smooth projective variety of \(\mathbb{C}\)-dimension = 3. The author is motivated by the following problem: Assume that \(V\) is of general type. Then find some universal integer \(N\) such that \(|NK |\) defines a birational map where \(K\) is the canonical bundle of \(V\). For irregular 3-folds \(V\) of general type, the problem was settled by Kollár. Therefore, in this paper, the author concentrates on regular 3-folds \(V\) of general type, i.e. \(h^1 (V,{\mathcal O}_V) = 0\). Let \({\mathcal H}^2 : = H^0 (V, \Omega^2_V) \otimes_\mathbb{C} {\mathcal O}_V \subset \Omega^2_V\) be the subsheaf of \(\Omega^2_V\) spanned by \(H^0 (V, \Omega^2_V)\). It is clear that \[ \text{rank } {\mathcal H}^2 \leq 3. \] The main result of this paper is the following theorem: The above problem admits a positive answer for regular 3-folds \(V\) of general type, provided rank \({\mathcal H}^2 = 1\) or 3. Some discussion when rank \({\mathcal H}^2 = 2\) is carried out.
reviewed by: Tan Vovan
Mathematics Subject Classification ID: 14J30
zbMATH DE Number: 558989
zbMATH Keywords: regular 3-folds of general type
zbMATH Keywords: birational map
MaRDI profile type: Publication
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full work available at URL: s0012-7094-93-07132-3
OpenAlex ID: W1481257139
description: scientific article; zbMATH DE number 558989