1,512 research outputs found
On the cohomology of stable map spaces
We describe an approach to calculating the cohomology rings of stable map
spaces. The method we use is due to Akildiz-Carrell and employs a C^*-action
and a vector field which is equivariant with respect to this C^*-action. We
give an explicit description of the big Bialynicky-Birula cell of the
C^*-action on Mbar_00(P^n,d) as a vector bundle on Mbar_0d. This is used to
calculate explicitly the cohomology ring of Mbar_00(P^n,d) in the cases d=2 and
d=3. Of particular interest is the case as n approaches infinity.Comment: 63 page
Uniformization of Deligne-Mumford curves
We compute the fundamental groups of non-singular analytic Deligne-Mumford
curves, classify the simply connected ones, and classify analytic
Deligne-Mumford curves by their uniformization type. As a result, we find an
explicit presentation of an arbitrary Deligne-Mumford curve as a quotient
stack. Along the way, we compute the automorphism 2-groups of weighted
projective stacks . We also discuss connections
with the theory of F-groups, 2-groups, and Bass-Serre theory of graphs of
groups.Comment: 39 pages, 2 figure
The intrinsic normal cone
We suggest a construction of virtual fundamental classes of certain types of
moduli spaces.Comment: LaTeX, Postscript file available at
http://www.math.ubc.ca/people/faculty/behrend/inc.p
Integrable Boundaries, Conformal Boundary Conditions and A-D-E Fusion Rules
The minimal theories are labelled by a Lie algebra pair where
is of -- type. For these theories on a cylinder we conjecture a
complete set of conformal boundary conditions labelled by the nodes of the
tensor product graph . The cylinder partition functions are given
by fusion rules arising from the graph fusion algebra of . We
further conjecture that, for each conformal boundary condition, an integrable
boundary condition exists as a solution of the boundary Yang-Baxter equation
for the associated lattice model. The theory is illustrated using the
or 3-state Potts model.Comment: 4 pages, REVTe
Minimal model boundary flows and c=1 CFT
We consider perturbations of unitary minimal models by boundary fields.
Initially we consider the models in the limit as c -> 1 and find that the
relevant boundary fields all have simple interpretations in this limit. This
interpretation allows us to conjecture the IR limits of flows in the unitary
minimal models generated by the fields \phi_{rr} of `low' weight. We check this
conjecture using the truncated conformal space approach. In the process we find
evidence for a new series of integrable boundary flows.Comment: (latex2e, 27 pages, 17 figures
The symplectic Deligne-Mumford stack associated to a stacky polytope
We discuss a symplectic counterpart of the theory of stacky fans. First, we
define a stacky polytope and construct the symplectic Deligne-Mumford stack
associated to the stacky polytope. Then we establish a relation between stacky
polytopes and stacky fans: the stack associated to a stacky polytope is
equivalent to the stack associated to a stacky fan if the stacky fan
corresponds to the stacky polytope.Comment: 20 pages; v2: To appear in Results in Mathematic
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