Projective normality of ruled surfaces

Euisung Park

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

Projective normality of ruled surfaces

Euisung Park^*

^*Corresponding author for this work

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

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-07-09121-6

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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.",

author = "Euisung Park",

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N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/77950614182

U2 - 10.1090/S0002-9939-07-09121-6

DO - 10.1090/S0002-9939-07-09121-6

M3 - Article

AN - SCOPUS:77950614182

SN - 0002-9939

VL - 136

SP - 839

EP - 847

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 3

ER -

Projective normality of ruled surfaces

Abstract

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