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28 March 2024
 
  » arxiv » 1410.5156

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Fundamental group of a geometric invariant theoretic quotient
Indranil Biswas ; Amit Hogadi ; A. J. Parameswaran ;
Date 20 Oct 2014
AbstractLet $M$ be an irreducible smooth projective variety, defined over an algebraically closed field, equipped with an action of a connected reductive affine algebraic group $G$, and let ${mathcal L}$ be a $G$--equivariant very ample line bundle on $M$. Assume that the GIT quotient $M/!!/G$ is a nonempty set. We prove that the homomorphism of algebraic fundamental groups $pi_1(M), longrightarrow, pi_1(M/!!/G)$, induced by the rational map $M, longrightarrow, M/!!/G$, is an isomorphism.
If $k,=, mathbb C$, then we show that the above rational map $M, longrightarrow , M/!!/G$ induces an isomorphism between the topological fundamental groups.
Source arXiv, 1410.5156
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