The connectedness of the moduli space of maps to homogeneous spaces

Details The connectedness of the moduli space of maps to homogeneous spaces The connectedness of the moduli space of maps to homogeneous spaces

2000-03-27

arxiv.org/abs/math/0003168v1

Mathematics

Algebraic Geometry

14 pages, LaTeX2e

Scientific paper

We prove the connectedness of the moduli space of maps (of fixed genus and homology class) to the homogeneous space G/P by degeneration via the maximal torus action. In the genus 0 case, the irreducibility of the moduli of maps is a direct consequence of connectedness. An analysis of a related Bialynicki-Birula stratification of the map space yields a rationality result: the (coarse) moduli space of genus 0 maps to G/P is a rational variety. The rationality argument depends essentially upon rationality results for quotients of SL2 representations proven by Katsylo and Bogomolov.

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