Homotopy exact sequences and orbifolds

Mitsui, Kentaro

doi:10.2140/ant.2015.9.1089

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Homotopy exact sequences and orbifolds

Kentaro Mitsui

Vol. 9 (2015), No. 5, 1089–1136

DOI: 10.2140/ant.2015.9.1089

Abstract

We generalize the homotopy exact sequences of étale fundamental groups for proper separable fibrations to the case where fibrations are not necessarily proper and separable. To treat the case where fibrations admit nonreduced geometric fibers, we introduce orbifolds within the framework of schemes and study their fundamental groups. As an application, we give a criterion for simple-connectedness of elliptic surfaces over an algebraically closed field by classifying simply connected orbifold curves.

Keywords

orbifolds, elliptic surfaces, coverings of curves, étale fundamental groups, homotopy exact sequences, simply connected

Mathematical Subject Classification 2010

Primary: 14F35

Secondary: 14D06, 14J27, 14H30

Milestones

Received: 8 October 2014

Revised: 21 January 2015

Accepted: 11 March 2015

Published: 21 June 2015

Authors

Kentaro Mitsui
Department of Mathematics Graduate School of Science Kobe University Hyogo 657-8501 Japan

Vol. 9, No. 5, 2015