832 research outputs found
Chern classes of Deligne-Mumford stacks and their coarse moduli spaces
Let be a complex projective algebraic variety with Gorenstein quotient
singularities and \X a smooth Deligne-Mumford stack having as its coarse
moduli space. We show that the CSM class coincides with the
pushforward to of the total Chern class c(T_{I\X}) of the inertia stack
I\X. We also show that the stringy Chern class of , whenever
is defined, coincides with the pushforward to of the total Chern class
c(T_{II\X}) of the double inertia stack II\X. Some consequences concerning
stringy/orbifold Hodge numbers are deduced.Comment: v1:Preliminary version, comments are very welcome! v2: Revised and
slightly expanded versio
On degree zero elliptic orbifold Gromov-Witten invariants
We compute, by two methods, the genus one degree zero orbifold Gromov-Witten
invariants with non-stacky insertions which are exceptional cases of the
dilaton and divisor equations. One method involves a detailed analysis of the
relevant moduli spaces. The other method, valid in the presence of torus
actions with isolated fixed points, is virtual localization. These computations
verify the conjectural evaluations of these invariants. Some genus one twisted
orbifold Gromov-Witten invariants are also computed.Comment: v1: 17 pages; v2: revision, 18 pages; v3: minor changes, 19 page
The Integral (orbifold) Chow Ring of Toric Deligne-Mumford Stacks
In this paper we study the integral Chow ring of toric Deligne-Mumford
stacks. We prove that the integral Chow ring of a semi-projective toric
Deligne-Mumford stack is isomorphic to the Stanley-Reisner ring of the
associated stacky fan. The integral orbifold Chow ring is also computed. Our
results are illustrated with several examples.Comment: 26 page
Note on orbifold Chow ring of semi-projective toric Deligne-Mumford stacks
We prove a formula for the orbifold Chow ring of semi-projective toric DM
stacks, generalizing the orbifold Chow ring formula of projective toric DM
stacks by Borisov-Chen-Smith. We also consider a special kind of
semi-projective toric DM stacks, the Lawrence toric DM stacks. We prove that
the orbifold Chow ring of a Lawrence toric DM stack is isomorphic to the
orbifold Chow ring of its associated hypertoric DM stack studied in \cite{JT}.Comment: The proof of a proposition is revise
On computations of genus zero two-point descendant Gromov-Witten invariants
We present a method of computing genus zero two-point descendant
Gromov-Witten invariants via one-point invariants. We apply our method to
recover some of calculations of Zinger and Popa-Zinger, as well as to obtain
new calculations of two-point descendant invariants.Comment: 17 page
Higher genus Gromov-Witten theory of the Hilbert scheme of points of the plane and CohFTs associated to local curves
We study the higher genus equivariant Gromov-Witten theory of the Hilbert
scheme of n points of the plane. Since the equivariant quantum cohomology is
semisimple, the higher genus theory is determined by an R-matrix via the
Givental-Teleman classification of Cohomological Field Theories (CohFTs). We
uniquely specify the required R-matrix by explicit data in degree 0. As a
consequence, we lift the basic triangle of equivalences relating the
equivariant quantum cohomology of the Hilbert scheme and the
Gromov-Witten/Donaldson-Thomas correspondence for 3-fold theories of local
curves to a triangle of equivalences in all higher genera. The proof uses the
previously determined analytic continuation of the fundamental solution of the
QDE of the Hilbert scheme. The GW/DT edge of the triangle in higher genus
concerns new CohFTs defined by varying the 3-fold local curve in the moduli
space of stable curves.
The equivariant orbifold Gromov-Witten theory of the symmetric product of the
plane is also shown to be equivalent to the theories of the triangle in all
genera. The result establishes a complete case of the crepant resolution
conjecture.Comment: 52 pages, 2 diagrams, Forum of Math. Pi (to appear
Integrating Lie algebroids via stacks
Lie algebroids can not always be integrated into Lie groupoids. We introduce
a new object--``Weinstein groupoid'', which is a differentiable stack with
groupoid-like axioms. With it, we have solved the integration problem of Lie
algebroids. It turns out that every Weinstein groupoid has a Lie algebroid and
every Lie algebroid can be integrated into a Weinstein groupoid.Comment: a proof improve
K-theoretic quasimap invariants and their wall-crossing
For each positive rational number , we define -theoretic
-stable quasimaps to certain GIT quotients W\sslash G. For
, this recovers the -theoretic Gromov-Witten theory of W\sslash
G introduced in more general context by Givental and Y.-P. Lee.
For arbitrary and in different stability chambers,
these -theoretic quasimap invariants are expected to be related by
wall-crossing formulas. We prove wall-crossing formulas for genus zero
-theoretic quasimap theory when the target W\sslash G admits a torus
action with isolated fixed points and isolated one-dimensional orbits.Comment: 20 page
The Crepant Transformation Conjecture implies the Monodromy Conjecture
In this note we prove that the crepant transformation conjecture for a
crepant birational transformation of Lawrence toric DM stacks studied in
\cite{CIJ} implies the monodromy conjecture for the associated wall crossing of
the symplectic resolutions of hypertoric stacks, due to Braverman, Maulik and
Okounkov.Comment: 18 pages, Referee's corrections and improvement
Integrating Poisson manifolds via stacks
A symplectic groupoid determines a Poisson
structure on . In this case, we call a symplectic groupoid of the
Poisson manifold . However, not every Poisson manifold has such a
symplectic groupoid. This keeps us away from some desirable goals: for example,
establishing Morita equivalence in the category of all Poisson manifolds. In
this paper, we construct symplectic Weinstein groupoids which provide a
solution to the above problem (Theorem \ref{main}). More precisely, we show
that a symplectic Weinstein groupoid induces a Poisson structure on its base
manifold, and that to every Poisson manifold there is an associated symplectic
Weinstein groupoid
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