Projective normality of ruled surfaces

Euisung Park

doi:10.1090/S0002-9939-07-09121-6

Projective normality of ruled surfaces

Euisung Park

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

In this article we study normal generation of irrational ruled surfaces. When C is a smooth curve of genus g, Green and Lazarsfeld proved that a very ample line bundle L ε PicX with deg(L) ≥ 2g+1-2h¹(X,L)- Cliff(X) is normally generated where Cliff(C) denotes the Clifford index of the curve C (Green and Lazarsfeld, 1986). We generalize this to line bundles on a ruled surface over C.

Original language	English
Pages (from-to)	839-847
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	136
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-07-09121-6
Publication status	Published - 2008 Mar

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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title = "Projective normality of ruled surfaces",

abstract = "In this article we study normal generation of irrational ruled surfaces. When C is a smooth curve of genus g, Green and Lazarsfeld proved that a very ample line bundle L ε PicX with deg(L) ≥ 2g+1-2h1(X,L)- Cliff(X) is normally generated where Cliff(C) denotes the Clifford index of the curve C (Green and Lazarsfeld, 1986). We generalize this to line bundles on a ruled surface over C.",

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AB - In this article we study normal generation of irrational ruled surfaces. When C is a smooth curve of genus g, Green and Lazarsfeld proved that a very ample line bundle L ε PicX with deg(L) ≥ 2g+1-2h1(X,L)- Cliff(X) is normally generated where Cliff(C) denotes the Clifford index of the curve C (Green and Lazarsfeld, 1986). We generalize this to line bundles on a ruled surface over C.

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Projective normality of ruled surfaces

Abstract

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