Measuring Singularities with Frobenius: The Basics

Angélica Benito (), Eleonore Faber () and Karen E. Smith ()
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Angélica Benito: University of Michigan, Department of Mathematics
Eleonore Faber: University of Toronto at Scarborough, Department of computer and mathematical science
Karen E. Smith: University of Michigan, Department of Mathematics

A chapter in Commutative Algebra, 2013, pp 57-97 from Springer

Abstract: Abstract The multiplicity is an important first step in measuring singularities, but it is too crude to give a good measurement. This paper describes the first steps toward understanding a much more subtle measure of singularities which arises naturally in three different contexts - analytic, algebro-geometric, and finally, algebraic. Miraculously, all three approaches lead to essentially the same measurement of singularities: the log canonical threshold (in characteristic zero) and the closely related F-pure threshold (in characteristic p).

Keywords: Characteristic Zero; Test Ideal; Multiplier Ideal; Canonical Divisor; Birational Geometry (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-5292-8_3

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DOI: 10.1007/978-1-4614-5292-8_3

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