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(Log) twisted curves

Published online by Cambridge University Press:  26 March 2007

Martin C. Olsson
Martin C. Olsson
Affiliation:
Department of Mathematics 3840, University of California, Berkeley, CA 94720-3840, USA [email protected]
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Abstract

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We describe an equivalence between the notion of balanced twisted curve introduced by Abramovich and Vistoli, and a new notion of log twisted curve, which is a nodal curve equipped with some logarithmic data in the sense of Fontaine and Illusie. As applications of this equivalence, we construct a universal balanced twisted curve, prove that a balanced twisted curve over a general base scheme admits étale locally on the base a finite flat cover by a scheme, and also give a new construction of the moduli space of stable maps into a Deligne–Mumford stack and a new proof that it is bounded.

Keywords

twisted curveslogarithmic geometrymoduli of stable maps14H1014D20
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 2 , March 2007 , pp. 476 - 494
Copyright
Foundation Compositio Mathematica 2007