Seshadri constants and the spaces of curves with prescribed singularities and positions

Yun Gao; Sheng Li Tan

doi:10.1007/s11425-010-4124-2

Seshadri constants and the spaces of curves with prescribed singularities and positions

Yun Gao, Sheng Li Tan^*

^*Corresponding author for this work

School of Mathematical Sciences

Shanghai Jiao Tong University

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

Abstract

We will give optimal bounds for Seshadri constants of an ample line bundle at multiple points on a complex projective surface X. We also present a solution to the long-studied classical problem on the existence of curves on X with given topological singularities at r arbitrary points p₁,...,p_r. Namely, we obtain a universal lower bound on the degree of curves for the existence. It is independent of the position of the singular points.

Original language	English
Pages (from-to)	1611-1620
Number of pages	10
Journal	Science China Mathematics
Volume	54
Issue number	8
DOIs	https://doi.org/10.1007/s11425-010-4124-2
State	Published - Aug 2011

Keywords

Seshadri constant
curve singularities
k-very ample
topological type

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10.1007/s11425-010-4124-2

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abstract = "We will give optimal bounds for Seshadri constants of an ample line bundle at multiple points on a complex projective surface X. We also present a solution to the long-studied classical problem on the existence of curves on X with given topological singularities at r arbitrary points p1,...,pr. Namely, we obtain a universal lower bound on the degree of curves for the existence. It is independent of the position of the singular points.",

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author = "Yun Gao and Tan, \{Sheng Li\}",

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AU - Tan, Sheng Li

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AB - We will give optimal bounds for Seshadri constants of an ample line bundle at multiple points on a complex projective surface X. We also present a solution to the long-studied classical problem on the existence of curves on X with given topological singularities at r arbitrary points p1,...,pr. Namely, we obtain a universal lower bound on the degree of curves for the existence. It is independent of the position of the singular points.

KW - Seshadri constant

KW - curve singularities

KW - k-very ample

KW - topological type

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DO - 10.1007/s11425-010-4124-2

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SP - 1611

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JO - Science China Mathematics

JF - Science China Mathematics

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ER -

Seshadri constants and the spaces of curves with prescribed singularities and positions

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Keywords

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