#### Date of Award

2011

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mathematics

#### Advisor(s)

Steven P. Diaz

#### Keywords

Algebra, Geometry

#### Subject Categories

Mathematics

#### Abstract

In the moduli space of curves of genus 3, the locus of hyperelliptic curves forms a divisor, that is a closed subscheme of codimension 1. J. Harris and I. Morrison compute an expression for the class of this divisor, in the Chow ring of the moduli space, using a map of vector bundles and by applying the Thom-Porteous formula to determine an expression for a certain degeneracy locus of this map. One would like to extend their idea in order to compute an expression for the divisor associated to the closure of the hyperelliptic locus, in the Chow ring of the moduli space of stable curves (of genus 3.) Recent work due to S. Diaz allows one to define the degeneracy class of a map between coherent sheaves, and gives explicit means for computing this class. Diaz uses his technique to partially extend the above mentioned computation, but he points out that in order to complete the computation one must combine his techniques with an Excess Thom-Porteous formula. This thesis completes this computation by combining the work of Diaz with this Excess Thom-Porteous formula.

#### Access

Open Access

#### Recommended Citation

Bleier, Thomas S., "Excess Porteous, Coherent Porteous, and the Hyperelliptic Locus in M3" (2011). *Mathematics - Dissertations*. 67.

http://surface.syr.edu/mat_etd/67