The Geometry of Stable Quotients in Genus One

Details The Geometry of Stable Quotients in Genus One The Geometry of Stable Quotients in Genus One

2011-09-02

arxiv.org/abs/1109.0331v1

Mathematics

Algebraic Geometry

36 pages

Scientific paper

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.

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