Stable maps and Hurwitz schemes in mixed characteristic

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In this short note, we propose a definition of complete Hurwitz schemes (and stacks) in mixed characteristic. We follow an idea of R. Pandharipande, and define the complete Hurwitz stack as a substack of stable maps of degree d of nodal pointed curves of genus g to the universal curve over the moduli stack of stable pointed curves of genus h. This substack is simply the closure of the locus of Hurwitz covers in characteristic 0. We describe in detail the reduction modulo 2 of the complete Hurwitz stack of genus 1 double covers of the projective line. The result is wilder than you would imagine in your wildest dreams. We end by speculating about a possible relationship with the work of Abramovich-Vistoli about stable maps into Deligne-Mumford stacks.
preliminatry version, 8 pages, 4 figures

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Algebraic Geometry, Number Theory, 14H10; 14H25; 14H30

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http://salesiana.dossiersoluciones.com/handle/123456789/77290

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9808074
 http://arxiv.org/abs/math/9808074

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arXiv