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Speaker:
Anton Leykin, University of Illinois at Chicago
Title:
Computing characteristic cycles of local cohomology modules
Abstract:
Characteristic cycles (CCs) can be used to examine the support of holonomic
D-modules, in particular, detect the vanishing.
I will discuss two approaches to computation of CCs of localizations and local
cohomology modules: the straightforward method that uses Grobner bases
techniques in (non-commutative) Weyl algebra and a novel approach (joint work
with Josep Alvarez Montaner) with
computations carried out in (commutative) polynomial rings.
For the former, I will recall algorithms due to Oaku, Takayama, and Walther that
compute the localization of a holonomic D-module and its local cohomology. The
latter will be accompanied by examples of computations of local
cohomology CCs in Macaulay 2.
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