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A vanishing theorem and symbolic powers of planar point ideals

Part of: Cycles and subschemes Curves (Co)homology theory General commutative ring theory Arithmetic rings and other special rings Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  01 October 2013

M. Dumnicki ,
T. Szemberg  and
H. Tutaj-Gasińska
M. Dumnicki
Affiliation:
Institute of Mathematics,Jagiellonian University,Łojasiewicza 6, PL-30-348 Kraków,Poland email marcin.dumnicki@im.uj.edu.plhalszka.tutaj@im.uj.edu.pl
T. Szemberg
Affiliation:
Institute of Mathematics,Pedagogical University of Cracow,Podchorazych 2, PL-30-084 Cracow,Poland email szemberg@up.krakow.pl
H. Tutaj-Gasińska
Affiliation:
Institute of Mathematics,Jagiellonian University,Łojasiewicza 6, PL-30-348 Kraków,Poland email marcin.dumnicki@im.uj.edu.plhalszka.tutaj@im.uj.edu.pl

Abstract

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The purpose of this paper is twofold. We present first a vanishing theorem for families of linear series with base ideal being a fat points ideal. We then apply this result in order to give a partial proof of a conjecture raised by Bocci, Harbourne and Huneke concerning containment relations between ordinary and symbolic powers of planar point ideals.

MSC classification

Secondary: 14C20: Divisors, linear systems, invertible sheaves 14F17: Vanishing theorems 14H50: Plane and space curves 14J26: Rational and ruled surfaces 13A15: Ideals; multiplicative ideal theory 13F20: Polynomial rings and ideals; rings of integer-valued polynomials
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 16 , October 2013 , pp. 373 - 387
Copyright
© The Author(s) 2013 

References

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