Characters of equivariant -modules on Veronese cones
Author:
Claudiu Raicu
Journal:
Trans. Amer. Math. Soc. 369 (2017), 2087-2108
MSC (2010):
Primary 13D45, 14M17, 14F10, 14F40
DOI:
https://doi.org/10.1090/tran/6713
Published electronically:
May 3, 2016
MathSciNet review:
3581228
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: For , we consider the Veronese map of degree
on a complex vector space
,
,
, and denote its image by
. We describe the characters of the simple
-equivariant holonomic
-modules supported on
. In the case when
, we obtain a counterexample to a conjecture of Levasseur by exhibiting a
-equivariant
-module on the Capelli type representation
which contains no
-invariant sections. We also study the local cohomology modules
, where
is the ring of polynomial functions on the vector space
. We recover a result of Ogus showing that there is only one local cohomology module that is non-zero (namely in degree
), and moreover we prove that it is a simple
-module and determine its character.
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Additional Information
Claudiu Raicu
Affiliation:
Department of Mathematics, University of Notre Dame, 255 Hurley, Notre Dame, Indiana 46556 – and – Institute of Mathematics “Simion Stoilow” of the Romanian Academy, Bucharest, Romania
Email:
craicu@nd.edu
DOI:
https://doi.org/10.1090/tran/6713
Keywords:
$\mathcal{D}$-modules,
Veronese cones,
local cohomology
Received by editor(s):
December 28, 2014
Received by editor(s) in revised form:
April 4, 2015
Published electronically:
May 3, 2016
Article copyright:
© Copyright 2016
American Mathematical Society