Charles Cadman

Using stacks to impose tangency conditions on curves

We define a Deligne-Mumford stack XD,r which depends on a scheme X, an effective Cartier divisor D ⊂ X, and a positive integer r. Then we show that the Abramovich-Vistoli moduli stack of stable maps into XD,r provides compactifications of the locally closed substacks of M g,n(X, β) corresponding to relative stable maps.

Gerby localization, Z3-Hodge integrals and the GW theory of [C³/Z3]

We exhibit a set of recursive relations that completely determine all equivariant Gromov-Witten invariants of

Quantum cohomology of [C^N/\mu_r]

[{\Bbb C}^3/{\Bbb Z}_3]

Quantum cohomology of [ N / μ r ]

. We interpret such invariants as

Quantum cosmology of [CN/μr]

{\Bbb Z}_3

Quantum cosmology of [C N / μ r ]

-Hodge integrals, and produce relations among them via Atiyah-Bott localization on moduli spaces of twisted stable maps to gerbes over~

Counting the hyperplane sections with fixed invariants of a plane quintic – three approaches to a classical enumerative problem

{\Bbb P}^1

The Orbifold Topological Vertex

.

Gromov-Witten invariants of P^2-stacks

We give a construction of the moduli space of stable maps to the classifying stack B\mu_r of a cyclic group by a sequence of r-th root constructions on M_{0, n}. We prove a closed formula for the total Chern class of \mu_r-eigenspaces of the Hodge bundle, and thus of the obstruction bundle of the genus zero Gromov-Witten theory of stacks of the form [C^N/\mu_r]. We deduce linear recursions for all genus-zero Gromov-Witten invariants.

Enumeration Of Rational Plane Curves Tangent To A Smooth Cubic

We give a construction of the moduli space of stable maps to the classifying stack B\mu_r of a cyclic group by a sequence of r-th root constructions on M_{0, n}. We prove a closed formula for the total Chern class of \mu_r-eigenspaces of the Hodge bundle, and thus of the obstruction bundle of the genus zero Gromov-Witten theory of stacks of the form [C^N/\mu_r]. We deduce linear recursions for all genus-zero Gromov-Witten invariants.