Genus-one stable maps, local equations, and Vakil–Zinger’s desingularization

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

We describe an algebro-geometric approach to Vakil-Zinger’s desingularization of the main component of the moduli of genus one stable maps to P [6, 7]. The new approach provides complete local structural results for this moduli space as well as for the desingularization of the entire moduli space and should fully extend to higher genera.

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

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(...

Constructive General Neron Desingularization for one dimensional local rings

An algorithmic proof of General Neron Desingularization is given here for one dimensional local rings and it is implemented in Singular. Also a theorem recalling Greenberg’ strong approximation theorem is presented for one dimensional local rings.

Relative Compactness and Product Stable Quotient Maps