COHOMOLOGY OF THE FLAG VARIETY UNDER PBW DEGENERATIONS

COHOMOLOGY OF THE FLAG VARIETY UNDER PBW DEGENERATIONS Transformation Groups Springer Science+Business Media New York (2018) COHOMOLOGY OF THE FLAG VARIETY UNDER PBW DEGENERATIONS MARTINA LANINI ELISABETTA STRICKLAND Dipartimento di Matematica Dipartimento di Matematica Universit a di Roma \Tor Vergata" Universit a di Roma \Tor Vergata" Via della Ricerca Scienti ca 1, Via della Ricerca Scienti ca 1, I-00133 Rome, Italy I-00133 Rome, Italy lanini@mat.uniroma2.it strickla@mat.uniroma2.it Abstract. PBW degenerations are a particularly nice family of proper at degenerations of type A ag varieties. We show that the cohomology of any PBW degeneration of the ag variety surjects onto the cohomology of the original ag variety, and that this holds in an equivariant setting too. We also prove that the same is true in the symplectic setting when considering Feigin's linear degeneration of the symplectic ag variety. 1. Introduction Degenerate ag varieties were introduced by Feigin in [Fei] by Lie theoretic methods, and extensively investigated afterwards, from several viewpoints. In type A they admit a linear algebraic description, which inspired a series of papers [CFR12], [CFR13], by Cerulli Irelli, Feigin and Reineke, where they produce a realisation of these degenerations in terms of quiver Grassmannians which was exploited, for example, to produce a cellularization or to study the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Transformation Groups Springer Journals

COHOMOLOGY OF THE FLAG VARIETY UNDER PBW DEGENERATIONS

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Topological Groups, Lie Groups; Algebra
ISSN
1083-4362
eISSN
1531-586X
D.O.I.
10.1007/s00031-018-9484-7
Publisher site
See Article on Publisher Site

Abstract

Transformation Groups Springer Science+Business Media New York (2018) COHOMOLOGY OF THE FLAG VARIETY UNDER PBW DEGENERATIONS MARTINA LANINI ELISABETTA STRICKLAND Dipartimento di Matematica Dipartimento di Matematica Universit a di Roma \Tor Vergata" Universit a di Roma \Tor Vergata" Via della Ricerca Scienti ca 1, Via della Ricerca Scienti ca 1, I-00133 Rome, Italy I-00133 Rome, Italy lanini@mat.uniroma2.it strickla@mat.uniroma2.it Abstract. PBW degenerations are a particularly nice family of proper at degenerations of type A ag varieties. We show that the cohomology of any PBW degeneration of the ag variety surjects onto the cohomology of the original ag variety, and that this holds in an equivariant setting too. We also prove that the same is true in the symplectic setting when considering Feigin's linear degeneration of the symplectic ag variety. 1. Introduction Degenerate ag varieties were introduced by Feigin in [Fei] by Lie theoretic methods, and extensively investigated afterwards, from several viewpoints. In type A they admit a linear algebraic description, which inspired a series of papers [CFR12], [CFR13], by Cerulli Irelli, Feigin and Reineke, where they produce a realisation of these degenerations in terms of quiver Grassmannians which was exploited, for example, to produce a cellularization or to study the

Journal

Transformation GroupsSpringer Journals

Published: May 29, 2018

References

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