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Full-Text Articles in Physical Sciences and Mathematics
Bernstein-Sato Polynomials In Commutative Algebra, Josep Àlvarez Montaner, Jack Jeffries, Luis Núñez-Betancourt
Bernstein-Sato Polynomials In Commutative Algebra, Josep Àlvarez Montaner, Jack Jeffries, Luis Núñez-Betancourt
Department of Mathematics: Faculty Publications
This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra.
On The Bounded Negativity Conjecture And Singular Plane Curves, Alexandru Dimca, Brian Harbourne, Gabriel Sticlaru
On The Bounded Negativity Conjecture And Singular Plane Curves, Alexandru Dimca, Brian Harbourne, Gabriel Sticlaru
Department of Mathematics: Faculty Publications
There are no known failures of Bounded Negativity in characteristic 0. In the light of recent work showing the Bounded Negativity Conjecture fails in positive characteristics for rational surfaces, we propose new characteristic free conjectures as a replacement. We also develop bounds on numerical characteristics of curves constraining their negativity. For example, we show that the H-constant of a rational curve C with at most 9 singular points satisfies H(C) > -2 regardless of the characteristic.