Recent work of Ein-Lazarsfeld-Smith and Hochster-Hunekeraised the problem of determining which symbolic powers of an idealare contained in a given ordinary power of the ideal.Bocci-Harbourne defined a quantity called the resurgence to address this problemfor homogeneous ideals in polynomial rings, witha focus on zero dimensionalsubschemes of projective space; the methods and resultsobtained there have much less to say about higher dimensional subschemes.Here we take the first steps toward extending this work to higher dimensionalsubschemes. We introduce new asymptoticversions of the resurgence and obtain upper and lower boundson them for ideals of smooth subschemes,generalizing what is done in \cite{BH}. We apply these boundsto ideals of unions of general lines in $\pr^N$.We also pose a Nagata type conjecture for symbolic powers of ideals oflines in $\pr^3$.
Asymptotic resurgences for ideals of positive dimensional subschemes of projective space
GUARDO, ELENA MARIA;
2013-01-01
Abstract
Recent work of Ein-Lazarsfeld-Smith and Hochster-Hunekeraised the problem of determining which symbolic powers of an idealare contained in a given ordinary power of the ideal.Bocci-Harbourne defined a quantity called the resurgence to address this problemfor homogeneous ideals in polynomial rings, witha focus on zero dimensionalsubschemes of projective space; the methods and resultsobtained there have much less to say about higher dimensional subschemes.Here we take the first steps toward extending this work to higher dimensionalsubschemes. We introduce new asymptoticversions of the resurgence and obtain upper and lower boundson them for ideals of smooth subschemes,generalizing what is done in \cite{BH}. We apply these boundsto ideals of unions of general lines in $\pr^N$.We also pose a Nagata type conjecture for symbolic powers of ideals oflines in $\pr^3$.File | Dimensione | Formato | |
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