Aleksey Zinger

A desingularization of the moduli space of stable genus-1 maps

The main component of the moduli space of stable genus-1 maps to projective space is the closure of the space of such maps that have smooth domains. Thus, counts of genus-1 curves (rather than the Gromov-Witten invariants) in the projective space correspond to integrals over this space. However, such integrals arise in the Gromov-Witten theory as well. In contrast to the genus-0 case, the main component is only part of the entire moduli space of genus-1 maps and is singular. I will describe a natural desingularization of the main component and of certain sheafs on the main component. Combined with the classical localization theorem and recent results in the GW-theory, these desingularizations make it possible to compute genus-1 enumerative invariants of projective spaces and Gromov-Witten invariants of complete intersections.