Bounding curves in algebraic surfaces by genus and Chern numbers
type: Item
instance of: scholarly article
title: Bounding curves in algebraic surfaces by genus and Chern numbers
zbMATH Open document ID: 0870.14020
author: Steven Lu
author: Yoichi Miyaoka
published in: Mathematical Research Letters
publication date: 1996-05-09T00:00:00Z
review text: An increasing interest in the theory of algebraic surfaces \(S\) is devoted to the understanding of which curves of fixed geometric genus are contained in \(S\). The general philosophy suggests that when \(S\) is of general type, then it may contain only few curves of low genus; in this context, \textit{F. A. Bogomolov} proved results on the boundedness of families of such curves. In the present paper, the authors use the Miyaoka-Yau inequality for the log cotangent sheaf \(\Omega_S(\)log\(C\)) to obtain finer results on the genus of curves in \(S\); in particular, their bounds show that in a surface of general type, there are finitely many rational or elliptic curves with fixed number of ordinary singularities of multiplicity \(\leq 3\).
reviewed by: Luca Chiantini
Mathematics Subject Classification ID: 14H25
Mathematics Subject Classification ID: 14J29
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 858516
zbMATH Keywords: curves in algebraic surfaces
zbMATH Keywords: Chern numbers
zbMATH Keywords: low genus
zbMATH Keywords: Miyaoka-Yau inequality
zbMATH Keywords: surface of general type
MaRDI profile type: Publication
DOI: 10.4310/MRL.1995.V2.N6.A1
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description: scientific article; zbMATH DE number 858516