Orbifold quantum Riemann–Roch, Lefschetz and Serre
- Hsian-Hua Tseng
- Mathematics
- 7 June 2005
Given a vector bundle $F$ on a smooth Deligne-Mumford stack $\X$ and an invertible multiplicative characteristic class $\bc$, we define the orbifold Gromov-Witten invariants of $\X$ twisted by $F$…
A mirror theorem for toric stacks
- T. Coates, A. Corti, H. Iritani, Hsian-Hua Tseng
- MathematicsCompositio Mathematica
- 15 October 2013
We prove a Givental-style mirror theorem for toric Deligne–Mumford stacks ${\mathcal{X}}$. This determines the genus-zero Gromov–Witten invariants of ${\mathcal{X}}$ in terms of an explicit…
Computing genus-zero twisted Gromov-Witten invariants
- T. Coates, A. Corti, H. Iritani, Hsian-Hua Tseng
- Mathematics
- 8 February 2007
Twisted Gromov-Witten invariants are intersection numbers in moduli spaces of stable maps to a manifold or orbifold X which depend in addition on a vector bundle over X and an invertible…
Abelian Hurwitz-Hodge integrals
- P. Johnson, R. Pandharipande, Hsian-Hua Tseng
- Mathematics
- 4 March 2008
Hodge classes on the moduli space of admissible covers with monodromy group G are
associated to irreducible representations of G. We evaluate all linear Hodge integrals over moduli
spaces of…
The quantum orbifold cohomology of weighted projective spaces
- T. Coates, A. Corti, Yuan-Pin Lee, Hsian-Hua Tseng
- Mathematics
- 20 August 2006
We calculate the small quantum orbifold cohomology of arbitrary weighted projective spaces. We generalize Givental’s heuristic argument, which relates small quantum cohomology to S1-equivariant Floer…
Integrating Lie algebroids via stacks
- Hsian-Hua Tseng, Chenchang Zhu
- MathematicsCompositio Mathematica
- 1 May 2004
Lie algebroids cannot always be integrated into Lie groupoids. We introduce a new structure, ‘Weinstein groupoid’, which may be viewed as stacky groupoids. We use this structure to present a solution…
Wall-crossings in toric Gromov–Witten theory I: crepant examples
- T. Coates, H. Iritani, Hsian-Hua Tseng
- Mathematics
- 17 November 2006
Let X be a Gorenstein orbifold with projective coarse moduli space X and let Y be a crepant resolution of X . We state a conjecture relating the genus-zero Gromov‐ Witten invariants of X to those of…
The Crepant Resolution Conjecture for Type A Surface Singularities
- T. Coates, A. Corti, H. Iritani, Hsian-Hua Tseng
- Mathematics
- 16 April 2007
Let X be an orbifold with crepant resolution Y. The Crepant Resolution Conjectures of Ruan and Bryan-Graber assert, roughly speaking, that the quantum cohomology of X becomes isomorphic to the…
The spaces of Laurent polynomials, Gromov-Witten theory of ℙ1-orbifolds and integrable hierarchies
- T. Milanov, Hsian-Hua Tseng
- Mathematics
- 2008
Abstract Let Mk,m be the space of Laurent polynomials in one variable , where k,m ≧ 1 are fixed integers and . According to B. Dubrovin [B. Dubrovin, Geometry of 2d topological field theories,…
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