# Irreducibility of \bar{M}_{0,n}(G/P,\beta)

@article{Thomsen1997IrreducibilityO, title={Irreducibility of \bar\{M\}\_\{0,n\}(G/P,\beta)}, author={Jesper Funch Thomsen}, journal={arXiv: Algebraic Geometry}, year={1997} }

Let G be a linear algebraic group, P be a parabolic subgroup of G and \beta be a cycle of dimension 1 in the Chow group of the quotient G/P. Using geometric arguments and Borel's fixed point theorem, we prove that the moduli space \bar{M}_{0,n}(G/P, \beta) of n-pointed genus 0 stable maps representing \beta is irreducible.

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On the irreducibility of the space of genus zero stable log maps to wonderful compactifications

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In this paper, we prove the moduli spaces of genus zero stable log maps to a large class of wonderful compactifications are irreducible and unirational.

#### References

Representations of algebraic groups

- Mathematics
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Part I. General theory: Schemes Group schemes and representations Induction and injective modules Cohomology Quotients and associated sheaves Factor groups Algebras of distributions Representations… Expand