288 research outputs found
The class of the bielliptic locus in genus 3
Let the bielliptic locus be the closure in the moduli space of stable curves
of the locus of smooth curves that are double covers of genus 1 curves. In this
paper we compute the class of the bielliptic locus in \bar{M}_3 in terms of a
standard basis of the rational Chow group of codimension-2 classes in the
moduli space. Our method is to test the class on the hyperelliptic locus: this
gives the desired result up to two free parameters, which are then determined
by intersecting the locus with two surfaces in \bar{M}_3.Comment: 14 pages, 2 figure
Prym varieties of genus four curves
Double covers of a generic genus four curve C are in bijection with Cayley
cubics containing the canonical model of C. The Prym variety associated to a
double cover is a quadratic twist of the Jacobian of a genus three curve X. The
curve X can be obtained by intersecting the dual of the corresponding Cayley
cubic with the dual of the quadric containing C. We take this construction to
its limit, studying all smooth degenerations and proving that the construction,
with appropriate modifications, extends to the complement of a specific divisor
in moduli. We work over an arbitrary field of characteristic different from two
in order to facilitate arithmetic applications.Comment: 30 pages; Some expository changes; removed erroneous (old) Thm 4.11
and changed (old) Thm 4.23 into (new) Thm 4.1
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