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FUNDAMENTAL GROUP OF A GEOMETRIC INVARIANT THEORETIC QUOTIENT

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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 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 π1(M) → π1(M//G), induced by the rational map M --→ M//G, is an isomorphism. If k = C, then we show that the above rational map M --→ M//G induces an isomorphism between the topological fundamental groups.

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  1. School of Mathematics, Tata Institute of Fundamental Research, Bombay, 400005, India

    INDRANIL BISWAS, AMIT HOGADI & A. J. PARAMESWARAN

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  1. INDRANIL BISWAS
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  2. AMIT HOGADI
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  3. A. J. PARAMESWARAN
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BISWAS, I., HOGADI, A. & PARAMESWARAN, A.J. FUNDAMENTAL GROUP OF A GEOMETRIC INVARIANT THEORETIC QUOTIENT. Transformation Groups 20, 367–379 (2015). https://doi.org/10.1007/s00031-015-9302-4

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