Computing Local Cohomology of Polynomial Rings of Characteristic Zero
Commutative Algebra and its Interaction with Algebraic Geometry (Notre Dame) May 22, 2023 - June 02, 2023
Computing Local Cohomology Of Polynomial Rings Of Characteristic Zero
Suppose R=KK[x_1,...,x_n] is a polynomial ring over a field KK of characteristic zero. If I is an ideal in R, then the local cohomology modules H^j_I(R) can be computed (at least in principle) in Macaulay2. In this talk we discuss the basic ideas that go into this (Groebner basis driven) algorithm. This involves a tour through the land of D-modules, with specific focus on the concept of Bernstein—Sato polynomials attached to elements f of R (which we will define and discuss).
Computing Local Cohomology Of Polynomial Rings Of Characteristic Zero
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