Computing jumping numbers in higher dimensions

2016/03/02 by Hans Baumers, Baumers, Hans, Ferran Dachs-Cadefau +1
Mathematics · #13H05 #14B05 #14F18 #14J17 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:13H05 #msc:14B05 #msc:14F18 #msc:14J17

paper · pdf · doi:10.48550/arxiv.1603.00787

24 pages

arxiv created 2016/03/02 · arxiv updated 2016/03/03

Abstract

The aim of this paper is to generalize the algorithm to compute jumping numbers on rational surfaces described in [AAD14] to varieties of dimension at least 3. Therefore, we introduce the notion of π-antieffective divisors, generalizing antinef divisors. Using these divisors, we present a way to find a small subset of the `classical' candidate jumping numbers of an ideal, containing all the jumping numbers. Moreover, many of these numbers are automatically jumping numbers, and in many other cases, it can be easily checked.

Related

• Jumping Numbers on Algebraic Surfaces with Rational Singularities
• Contribution of jumping numbers by exceptional divisors, with an appendix by Karen E. Smith and Kevin Tucker
• Jumping numbers of analytic multiplier ideals (with an appendix by Sébastien Boucksom)
• Jumping numbers of a simple complete ideal in a two-dimensional regular local ring
• Multiplier ideals in two-dimensional local rings with rational singularities