On the horizontal base locus of multiples of tautological sheaves of projectivised cotangent bundles. II
type: Item
instance of: scholarly article
title: On the horizontal base locus of multiples of tautological sheaves of projectivised cotangent bundles. II
zbMATH Open document ID: 0806.14028
DOI: 10.1007/BF02568347
author: Tie Luo
published in: Manuscripta Mathematica
publication date: 1995-02-13T00:00:00Z
full work available at URL: https://eudml.org/doc/155843
review text: The present paper is a continuation of part I [cf. Comment. Math. Helv. 66, No. 4, 580-589 (1991; Zbl 0769.14013)]. Let \(S\) be a minimal algebraic surface of general type, \(V\) the projectivised cotangent bundle. The horizontal base components of high multiples of \(L\), the tautological line bundle of \(V\), is studied. In the earlier paper a positive number \(t_ 0\), which depends on the coefficient of a base component along \(\pi^* K_ S\) in a standard decomposition of the component in \(\text{Pic} (V)\), is defined and bounds using Chern numbers of \(S\) are given. The problem of computing \(t_ 0\) is proposed. A partial solution to the problem is given in the present article. When \(L\) (or \(\Omega_ S)\) is nef, it is proved that \(t_ 0 = (c^ 2_ 1 - c_ 2)/c^ 2_ 1\). The techniques employed are based upon the Riemann- Roch theory for nef and big divisors. As an application the conjecture of Green and Griffiths in the case \(c^ 2_ 1 > {3 \over 2} c_ 2\) is verified; i.e. the images of nontrivial holomorphic curves in \(S\) are algebraically degenerated.
reviewed by: Tie Luo
Mathematics Subject Classification ID: 14J29
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 492749
zbMATH Keywords: bounds of Chern numbers
zbMATH Keywords: minimal algebraic surface of general type
zbMATH Keywords: tautological line bundle
zbMATH Keywords: Riemann-Roch
zbMATH Keywords: nef
zbMATH Keywords: big divisors
MaRDI profile type: Publication
cites work: Q5749404
cites work: Q4746076
cites work: Riemann-Roch Type Inequalities for NEF and Big Divisors
cites work: A note on the Hodge index theorem
cites work: The horizontal base locus of multiples of tautological sheaves of projectivised cotangent bundles
cites work: Q3979768
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description: scientific article; zbMATH DE number 492749