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.
Faber, C., Pagani, N. (2015). The class of the bielliptic locus in genus 3. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015(12), 3943-3961 [10.1093/imrn/rnu057].
The class of the bielliptic locus in genus 3
Pagani N.
2015
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
