caa a22 4500 605495939 CHVBK 20210128100533.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10231-013-0373-3 doi (NATIONALLICENCE)springer-10.1007/s10231-013-0373-3 The coarse moduli space of a flat analytic groupoid [Elektronische Daten] [Simone Borghesi, Giuseppe Tomassini] Let $$\mathcal X $$ X be a flat analytic groupoid $$R_X\stackrel{s}{\underset{t}{\rightrightarrows }}X$$ R X ⇉ t s X such that the holomorphic map $$j=(s,t):R_X\rightarrow X\times X$$ j = ( s , t ) : R X → X × X is finite. In this paper, we prove that there exist a (unique up to isomorphism) complex space $$Q(\mathcal X )$$ Q ( X ) and a holomorphic map $$q:X\rightarrow Q(\mathcal X )$$ q : X → Q ( X ) which is a GC quotient (see Definition3.1). 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). Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 Analytic groupoids nationallicence Several complex variables nationallicence Quotients of complex spaces nationallicence Coarse moduli space nationallicence Borghesi Simone Università degli Studi di Milano-Bicocca, Via Cozzi, 53, 20125, Milano, Italy aut Tomassini Giuseppe Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126, Pisa, Italy aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/1(2015-02-01), 247-257 0373-3114 194:1<247 2015 194 10231 https://doi.org/10.1007/s10231-013-0373-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-013-0373-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Borghesi Simone Università degli Studi di Milano-Bicocca, Via Cozzi, 53, 20125, Milano, Italy aut NATIONALLICENCE 700 1- Tomassini Giuseppe Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126, Pisa, Italy aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/1(2015-02-01), 247-257 0373-3114 194:1<247 2015 194 10231