Quantum Cohomology of Hilb2(P1xP1) and Enumerative Applications
Dalide Pontoni
Abstract
We compute the Small Quantum Cohomology of Hilb2(P1xP1) 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 P1xP1. This extends the results obtained by Graber for Hilb2(P2) and hyperelliptic curves in P2.
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