Moduli space of stable maps to projective space via GIT

Details Moduli space of stable maps to projective space via GIT Moduli space of stable maps to projective space via GIT

2007-11-30

arxiv.org/abs/0711.4929v2

Mathematics

Algebraic Geometry

22 pages. Introduction revised. Typos corrected

Scientific paper

We compare the Kontsevich moduli space of genus 0 stable maps to projective space with the quasi-map space when $d=3$. More precisely, we prove that when $d=3$, the obvious birational map from the quasi-map space to the moduli space of stable maps is the composition of three blow-ups followed by two blow-downs. Furthermore, we identify the blow-up/down centers explicitly in terms of the moduli spaces for lower degrees. Using this, we calculate the Betti numbers, the integral Picard group, and the rational cohomology ring. The degree two case is worked out as a warm-up.

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