Let (Formula presented.) be a flat analytic groupoid (Formula presented.) such that the holomorphic map (Formula presented.) is finite. In this paper, we prove that there exist a (unique up to isomorphism) complex space (Formula presented.) and a holomorphic map (Formula presented.) which is a GC quotient (see Definition 3.1). This extends to analytic groupoids the Main Theorem proved by Keel and Mori in the algebraic context (Keel and Mori in Ann Math 145(1):193–213, 1997, 1.1 Theorem).
Borghesi, S., Tomassini, G. (2015). The coarse moduli space of a flat analytic groupoid. ANNALI DI MATEMATICA PURA ED APPLICATA, 194(1), 247-257 [10.1007/s10231-013-0373-3].
The coarse moduli space of a flat analytic groupoid
BORGHESI, SIMONE;
2015
Abstract
Let (Formula presented.) be a flat analytic groupoid (Formula presented.) such that the holomorphic map (Formula presented.) is finite. In this paper, we prove that there exist a (unique up to isomorphism) complex space (Formula presented.) and a holomorphic map (Formula presented.) which is a GC quotient (see Definition 3.1). This extends to analytic groupoids the Main Theorem proved by Keel and Mori in the algebraic context (Keel and Mori in Ann Math 145(1):193–213, 1997, 1.1 Theorem).
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