F-thresholds and Bernstein–Sato Polynomials

By M. Mustaţă, S. Takagi, Kei-ichi Watanabe. 2004

129 citations recorded by the source corpus.

We introduce and study invariants of singularities in positive characteristic called F-thresholds. They give an analogue of the jumping coefficients of multiplier ideals in characteristic zero. We discuss the connection between the invariants of an ideal in characteristic zero and the invariants of the different reduction mod p of this ideal. Our main point is that this relation depends on arithmetic properties of p. We also describe a new connection between invariants mod p and the roots of the Bernstein-Sato polynomial.

Subfields: Mathematical Physics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0709ec645668b9bc9c272bd6a269a0d0fe54892e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. M. Mustaţă
2. Manuel Blickle
3. Karen E. Smith
4. Mircea Mustactva
5. Karl Schwede
6. S. Takagi
7. Craig Huneke
8. Kei-ichi Watanabe

In Numerical Analysis

1. M. Mustaţă
2. Manuel Blickle
3. Karl Schwede
4. Mircea Mustactva
5. Karen E. Smith

In Statistical and Nonlinear Physics

1. M. Mustaţă
2. Manuel Blickle
3. Karl Schwede
4. Mircea Mustactva
5. Karen E. Smith
6. S. Takagi

Citations in the corpus

• F-Thresholds, tight closure, integral closure, and multiplicity bounds (2007, background): “We refer to [BMS2], [HM], [HY], [ MTW ] and [TW] for further discussions.”
• IMPANGA lecture notes on log canonical thresholds (2011, methodology): “abe [TW] when the ambient variety is fairly general. In what follows we will focus on the case of ambient nonsingular varieties, in which case we can use a more direct asymptotic definition, following [MTW]. Let k be a perfect3 field of positive characteristic p. We consider a regular, finitely generat”
• F-thresholds of hypersurfaces (2007, methodology): “We refer to [ MTW ] for a discussion of the known and conjectural connections between the invariants in characteristic zero and those in characteristic p.”
• Discreteness and rationality of F-jumping numbers on singular varieties (2009, background): “for all �> 0. The set of F-jumping numbers, and in particular the first of these, called the F-pure threshold which is the analog of the log canonical threshold from characteristic zero, have been studied for example in [23,31, 32 ,48].”