The Geometry of Stable Quotients in Genus One
Algebraic Geometry
2011-09-05 v1
Abstract
Stable quotient spaces provide an alternative to stable maps for compactifying spaces of maps. When the target is projective space and the domain curve has genus 1, these are smooth proper Deligne-Mumford stacks. In this paper we study the associated coarse moduli schemes. We show these schemes are projective, rationally connected and have Picard number 2. Then we give generators for the Picard group, compute the canonical divisor, and the cones of ample and effective divisors. In certain cases, we also give a closed formula for the Poincar\'{e} polynomial.
Keywords
Cite
@article{arxiv.1109.0331,
title = {The Geometry of Stable Quotients in Genus One},
author = {Yaim Cooper},
journal= {arXiv preprint arXiv:1109.0331},
year = {2011}
}
Comments
36 pages