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The unirationality of the moduli spaces of curves of genus 14 or lower

Published online by Cambridge University Press:  04 December 2007

Alessandro Verra
Alessandro Verra
Affiliation:
Dipartimento di Matematica, Università di Roma Tre, Largo San Leonardo Murialdo 1, 00146 Roma, Italyverra@mat.uniroma3.it
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Abstract

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We prove the unirationality of the moduli space of complex curves of genus 14. The method essentially relies on linkage of curves. In particular it is shown that a general curve of genus 14 admits a projective model D, in a six-dimensional projective space, which is linked to a general curve C of degree 14 and genus 8 by a complete intersection of quadrics. Using this property we are able to obtain, after a reasonable amount of further work, the unirationality result in the case of genus 14. Moreover, some variations of the same method, involving the Hilbert schemes of curves of very low genus, are used to obtain the same result for the known cases of genus 11, 12, 13.

Keywords

moduli spaces of curvesunirationalityHilbert schemeslow genuslinked curvescomplete intersection14H10 (primary)14H45 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 6 , November 2005 , pp. 1425 - 1444
Copyright
Foundation Compositio Mathematica 2005