Surfaces fibrées en courbes de genre deux
type: Item
instance of: scholarly article
title: Surfaces fibrées en courbes de genre deux
zbMATH Open document ID: 0579.14028
author: Gang Xiao
published in: Lecture Notes in Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The book under review is devoted to a detailed study of surfaces representable in the form of a family of curves of genus 2 (with possible degenerations). The classification of surfaces with a pencil of rational or elliptic curves is classical, and the classification of surfaces with a pencil of curves of genus 2 (which is the simplest case of surfaces of general type) was begun by \textit{E. Horikawa} [cf. Complex Anal. Algeb. Geom., collect. Pap. dedic. K. Kodaira, 79-90 (1977; Zbl 0349.14021)] who considered them as double coverings of ruled surfaces. The author introduces numerical invariants of surfaces fibered into curves of genus 2 and examines the question of existence of surfaces with given numerical invariants. It is shown that a surface fibered into curves of genus 2 usually has general type; a list of all possible exceptions from this rule is given in section 4. For surfaces of general type there usually exists at most one pencil of curves of genus 2; the author gives a list of all possible exceptions which includes a surface with \(1+20\cdot 19/2=191\) pencils. Finally, the author studies canonical and bicanonical maps for surfaces with a pencil of curves of genus 2.
reviewed by: F. L. Zak
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14-02
Mathematics Subject Classification ID: 14H10
zbMATH DE Number: 3927090
zbMATH Keywords: classification of surfaces with a pencil of curves of genus 2
zbMATH Keywords: surfaces of general type
MaRDI profile type: Publication
DOI: 10.1007/BFB0075351
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description: scientific article; zbMATH DE number 3927090