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Localization of virtual classes

- T. Graber, R. Pandharipande
- Mathematics
- 1 August 1997

We prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories. As an application, the higher genus Gromov-Witten invariants of… Expand

Curve counting via stable pairs in the derived category

- R. Pandharipande, Richard P. Thomas
- Mathematics
- 16 July 2007

For a nonsingular projective 3-fold X, we define integer invariants virtually enumerating pairs (C,D) where C⊂X is an embedded curve and D⊂C is a divisor. A virtual class is constructed on the… Expand

Gromov–Witten theory and Donaldson–Thomas theory, I

- D. Maulik, N. Nekrasov, A. Okounkov, R. Pandharipande
- MathematicsCompositio Mathematica
- 2 December 2003

We conjecture an equivalence between the Gromov–Witten theory of 3-folds and the holomorphic Chern–Simons theory of Donaldson and Thomas. For Calabi–Yau 3-folds, the equivalence is defined by the… Expand

The tropical vertex

- M. Gross, R. Pandharipande, Bernd S Siebert
- Mathematics
- 4 February 2009

Elements of the tropical vertex group are formal families of symplectomorphisms of the 2-dimensional algebraic torus. We prove ordered product factorizations in the tropical vertex group are… Expand

Notes on stable maps and quantum cohomology

- W. Fulton, R. Pandharipande
- Mathematics
- 15 August 1996

These are notes from a jointly taught class at the University of Chicago and lectures by the first author in Santa Cruz. Topics covered include: construction of moduli spaces of stable maps,… Expand

Gromov-Witten theory, Hurwitz theory, and completed cycles

- A. Okounkov, R. Pandharipande
- Mathematics
- 24 April 2002

We establish an explicit equivalence between the stationary sector of the Gromov-Witten theory of a target curve X and the enumeration of Hurwitz coverings of X in the basis of completed cycles. The… Expand

Hodge integrals and Gromov-Witten theory

- C. Faber, R. Pandharipande
- Mathematics
- 30 October 1998

Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these… Expand

The local Gromov-Witten theory of curves

- J. Bryan, R. Pandharipande
- Mathematics
- 2 November 2004

The local Gromov-Witten theory of curves is solved by localization and degeneration methods. Localization is used for the exact evalu- ation of basic integrals in the local Gromov-Witten theory of P… Expand

Algebraic cobordism revisited

- M. Levine, R. Pandharipande
- Mathematics
- 8 May 2006

We define a cobordism theory in algebraic geometry based on normal crossing degenerations with double point singularities. The main result is the equivalence of double point cobordism to the theory… Expand

The moduli space of stable quotients

- A. Marian, D. Oprea, R. Pandharipande
- Mathematics
- 20 April 2009

A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck’s Quot scheme. Over nodal curves, a relative… Expand

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