A note on discreteness of -jumping numbers

Author:
Karl Schwede

Journal:
Proc. Amer. Math. Soc. **139** (2011), 3895-3901

MSC (2000):
Primary 13A35, 14F18, 14B05

Published electronically:
June 28, 2011

MathSciNet review:
2823035

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that is a ring essentially of finite type over a perfect field of characteristic and that is an ideal. We prove that the set of -jumping numbers of has no limit points under the assumption that is normal and -Gorenstein - we make no assumption as to whether the -Gorenstein index is divisible by . Furthermore, we also show that the -jumping numbers of are discrete under the more general assumption that is -Cartier.

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Additional Information

**Karl Schwede**

Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802

Email:
schwede@math.psu.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-10825-6

Keywords:
Test ideal,
jumping number,
$\mathbb{Q}$-Gorenstein,
multiplier ideal

Received by editor(s):
April 8, 2010

Received by editor(s) in revised form:
October 4, 2010

Published electronically:
June 28, 2011

Additional Notes:
The author was partially supported by a National Science Foundation postdoctoral fellowship and by NSF grant DMS-1064485/0969145.

Communicated by:
Irena Peeva

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.