Quantum Cohomology of Hilb^2(P^1xP^1) and Enumerative Applications

Details Quantum Cohomology of Hilb^2(P^1xP^1) and Enumerative Applications Quantum Cohomology of Hilb^2(P^1xP^1) and Enumerative Applications

2004-07-29

arxiv.org/abs/math/0407508v1

Mathematics

Algebraic Geometry

30 pages

Scientific paper

We compute the Small Quantum Cohomology of Hilb^2(P^1xP^1) and determine
recursively most of the Big Quantum Cohomology. We prove a relationship between
the invariants so obtained and the enumerative geometry of hyperelliptic curves
in P^1xP^1. This extends the results obtained by Graber for Hilb^2(P^2) and
hyperelliptic curves in P^2.

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