Bernstein-Sato polynomials, especially of hyperplane arrangements in three variables - Daniel Bath скачать в хорошем качестве

Bernstein-Sato polynomials, especially of hyperplane arrangements in three variables - Daniel Bath

Talk by Daniel Bath (KU Leuven), at the Antwerp Algebra, Geometry and Number Theory Seminar on March 28, 2025. The Bernstein—Sato polynomial is an invariant of a hypersurface, that manages to simultaneously encode almost all other singularity invariants. Unfortunately, it is famously hard to compute and many of its roots hard to interpret. I will tell you what the Bernstein—Sato polynomial is and convince you why it is interesting. Then I will scare you by showing it is very hard to compute, even in the simplest examples. Then I will, hopefully, impress you some recent results; in particular, I will give a complete formula for the roots of the Bernstein—Sato polynomial of a hyperplane arrangement in three variables. It turns out it has only one possible non-combinatorially determined root whose root-hood is equivalent to a simple local cohomology vanishing criterion.