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Symmetries and stabilization for sheaves of vanishing cycles

Abstract:

Let $U$ be a smooth $\mathbb C$-scheme, $f:U\to\mathbb A^1$ a regular function, and $X=$Crit$(f)$ the critical locus, as a $\mathbb C$-subscheme of $U$. Then one can define the "perverse sheaf of vanishing cycles" $PV_{U,f}$, a perverse sheaf on $X$. This paper proves four main results: (a) Suppose $\Phi:U\to U$ is an isomorphism with $f\circ\Phi=f$ and $\Phi\vert_X=$id$_X$. Then $\Phi$ induces an isomorphism $\Phi_*:PV_{U,f}\to PV_{U,f}$. We show that $\Phi_*$ is multiplication by det$(d...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.5427/jsing.2015.11e

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
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Name:
Engineering and Physical Sciences Research Council
Grant:
EP/I033343/1
Publisher:
Worldwide Center of Mathematics
Journal:
Journal of Singularities More from this journal
Volume:
11
Pages:
85-151
Publication date:
2015-06-04
DOI:
ISSN:
1949-2006
Keywords:
Pubs id:
pubs:364010
UUID:
uuid:e8d6c20e-b6ee-4996-8962-0cf76429a316
Local pid:
pubs:364010
Source identifiers:
364010
Deposit date:
2013-11-17

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