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Fundamental group of a geometric invariant theoretic quotient | Indranil Biswas
; Amit Hogadi
; A. J. Parameswaran
; | Date: |
20 Oct 2014 | Abstract: | Let $M$ 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 | Services: | Forum | Review | PDF | Favorites |
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