Kawachi's invariant for fat points

Nobuo Hara

doi:10.1016/S0022-4049(00)00188-2

Kawachi's invariant for fat points

Nobuo Hara

SCI - Mathematics

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

Abstract

We extend Kawachi's invariant for reduced points on a normal suface to an invariant defined for possibly non-reduced zero-dimensional closed subschemes (or fat points) on a surface with rational singularities. We give an upper bound of this invariant in terms of the length of the fat point and the discrepancy of the minimal resolution. As an application we prove a Reider-type theorem for k-very ampleness on surfaces with rational singularities.

Original language	English
Pages (from-to)	201-211
Number of pages	11
Journal	Journal of Pure and Applied Algebra
Volume	165
Issue number	2
DOIs	https://doi.org/10.1016/S0022-4049(00)00188-2
Publication status	Published - 2001 Dec 7

Keywords

14C20
14F17
14J17

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/S0022-4049(00)00188-2

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title = "Kawachi's invariant for fat points",

abstract = "We extend Kawachi's invariant for reduced points on a normal suface to an invariant defined for possibly non-reduced zero-dimensional closed subschemes (or fat points) on a surface with rational singularities. We give an upper bound of this invariant in terms of the length of the fat point and the discrepancy of the minimal resolution. As an application we prove a Reider-type theorem for k-very ampleness on surfaces with rational singularities.",

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