558 research outputs found
A TQFT of Intersection Numbers on Moduli Spaces of Admissible Covers
We construct a two-level weighted TQFT whose structure coefficents are
equivariant intersection numbers on moduli spaces of admissible covers. Such a
structure is parallel (and strictly related) to the local Gromov-Witten theory
of curves of Bryan-Pandharipande. We compute explicitly the theory using
techniques of localization on moduli spaces of admissible covers of a
parametrized projective line. The Frobenius Algebras we obtain are one
parameter deformations of the class algebra of the symmetric group S_d. In
certain special cases we are able to produce explicit closed formulas for such
deformations in terms of the representation theory of S_d
Hodge-type integrals on moduli spaces of admissible covers
We study Hodge Integrals on Moduli Spaces of Admissible Covers. Motivation
for this work comes from Bryan and Pandharipande's recent work on the local GW
theory of curves, where analogouos intersection numbers, computed on Moduli
Spaces of Relative Stable Maps, are the structure coefficients for a
Topological Quantum Field Theory. Admissible Covers provide an alternative
compactification of the Moduli Space of Maps, that is smooth and doesn't
contain boundary components of excessive dimension. A parallel, yet different,
TQFT, can then be constructed. In this paper we compute, using localization,
the relevant Hodge integrals for admissible covers of a pointed sphere of
degree 2 and 3, and formulate a conjecture for general degree. In genus 0, we
recover the well-known Aspinwall Morrison formula in GW theory.Comment: This is the version published by Geometry & Topology Monographs on 21
September 200
A geometric perspective on the piecewise polynomiality of double Hurwitz numbers
We describe double Hurwitz numbers as intersection numbers on the moduli
space of curves. Assuming polynomiality of the Double Ramification Cycle (which
is known in genera 0 and 1), our formula explains the polynomiality in chambers
of double Hurwitz numbers, and the wall crossing phenomenon in terms of a
variation of correction terms to the {\psi} classes. We interpret this as
suggestive evidence for polynomiality of the Double Ramification Cycle.Comment: 15 pages, 5 figure
Counting Bitangents with Stable Maps
This paper is an elementary introduction to the theory of moduli spaces of
curves and maps. As an application to enumerative geometry, we show how to
count the number of bitangent lines to a projective plane curve of degree
by doing intersection theory on moduli spaces.Comment: expository- soft introduction to working with moduli. Many pictures.
To appear on Expositiones Mathematica
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