Genus-one Stable Maps, Local Equations, and Vakil-zinger’s Desingularization

A Desingularization of ( the Main Component of ) the Moduli Space of Genus - One Stable Maps into

Towards the Cohomology of Moduli Spaces of Higher Genus Stable Maps

We prove that the orbifold desingularization of the moduli space of stable maps of genus g = 1 recently constructed by Vakil and Zinger has vanishing rational cohomology groups in odd degree k < 10.

A Desingularization of the Main Component of the Moduli Space of Genus-One Stable Maps into Pn

We construct a natural smooth compactification of the space of smooth genus-one curves with k distinct points in a projective space. It can be viewed as an analogue of a well-known smooth compactification of the space of smooth genus-zero curves, i.e. the space of stable genus-zero maps M0,k(P , d). In fact, our compactification is obtained from the singular space of stable genus-one maps M1,k(...

A Natural Smooth Compactification of the Space of Elliptic Curves in Projective Space

The space of smooth genus 0 curves in projective space has a natural smooth compactification: the moduli space of stable maps, which may be seen as the generalization of the classical space of complete conics. In arbitrary genus, no such natural smooth model is expected, as the space satisfies “Murphy’s Law”. In genus 1, however, the situation remains beautiful. We give a natural smooth compact...

Recursions for Characteristic Numbers of Genus One Plane Curves

Characteristic numbers of families of maps of nodal curves to P are de ned as intersection of natural divisor classes. (This de nition agrees with the usual de nition for families of plane curves.) Simple recursions for characteristic numbers of genus one plane curves of all degrees are computed.