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MultiplierIdeals :: MultiplierIdeals

MultiplierIdeals -- A package for computing multiplier ideals

Description

MultiplierIdeals is a package for computing multiplier ideals, log canonical thresholds, and jumping numbers, using specialized routines wherever possible.

The package Dmodules provides computations of multiplier ideals, log canonical thresholds, and jumping numbers of arbitrary ideals using general algorithms.

This package provides alternatives for special classes of ideals, including monomial ideals, hyperplane arrangements, generic determinantal ideals, and binomial ideals (currently, ideals of curves in 3-space parametrized by monomials). These special computations are typically much faster than general methods and can often handle larger examples.

References

  • [BL] Blickle, Manuel and Lazarsfeld, Robert An informal introduction to multiplier ideals. Trends in commutative algebra, 87-114, Math. Sci. Res. Inst. Publ., 51, Cambridge Univ. Press, Cambridge, 2004.
  • [H] Howald, J.A. Multiplier ideals of monomial ideals. Trans. Amer. Math. Soc. 353 (2001), no. 7, 2665-2671
  • [J] Johnson, Amanda Multiplier ideals of determinantal ideals. Thesis (Ph.D.)-University of Michigan. 2003
  • [L] Lazarsfeld, Robert Positivity in algebraic geometry. II. 2004
  • [M] Mustațǎ Mircea Multiplier ideals of hyperplane arrangements. Trans. Amer. Math. Soc. 358 (2006), no. 11, 5015-5023.
  • [T] Teitler, Zach A note on Mustațǎ's computation of multiplier ideals of hyperplane arrangements. Proc. Amer. Math. Soc. 136 (2008), no. 5, 1575-1579.
  • [Th] Thompson, H.M. Multiplier Ideals of Monomial Space Curves, arXiv:1006.1915v4 [math.AG].

Authors

Version

This documentation describes version 1.0 of MultiplierIdeals.

Source code

The source code from which this documentation is derived is in the file MultiplierIdeals.m2.

Exports