Moduli stacks of stable toric quasimaps

Details Moduli stacks of stable toric quasimaps Moduli stacks of stable toric quasimaps

2009-08-31

arxiv.org/abs/0908.4446v2

Advances in Mathematics 225 (2010), 3022-3051

Mathematics

Algebraic Geometry

Published version

Scientific paper

10.1016/j.aim.2010.05.023

We construct new "virtually smooth" modular compactifications of spaces of maps from nonsingular curves to smooth projective toric varieties. They generalize Givental's compactifications, when the complex structure of the curve is allowed to vary and markings are included, and are the toric counterpart of the moduli spaces of stable quotients introduced by Marian, Oprea, and Pandharipande to compactify spaces of maps to Grassmannians. A brief discussion of the resulting invariants and their (conjectural) relation with Gromov-Witten theory is also included.

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