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Purity for graded potentials and quantum cluster positivity

Abstract:

Consider a smooth quasiprojective variety X equipped with a C*-action, and a regular function f : X → C which is C*-equivariant with respect to a positive weight action on the base. We prove the purity of the mixed Hodge structure and the hard Lefschetz theorem on the cohomology of the vanishing cycle complex of f on proper components of the critical locus of f, generalizing a result of Steenbrink for isolated quasi-homogeneous singularities. Building on wor...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1112/S0010437X15007332

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More from this funder
Funding agency for:
Szendroi, B
Grant:
EP/I033343/1
More from this funder
Funding agency for:
Szendroi, B
Grant:
EP/I033343/1
Publisher:
London Mathematical Society Publisher's website
Journal:
Compositio Mathematica Journal website
Volume:
151
Issue:
10
Pages:
1913-1944
Publication date:
2015-01-01
DOI:
EISSN:
1570-5846
ISSN:
0010-437X
Source identifiers:
517587
Keywords:
Pubs id:
pubs:517587
UUID:
uuid:41d57bc1-7a36-4d53-ac8b-3e3d6fde6ad2
Local pid:
pubs:517587
Deposit date:
2015-04-28

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