Theta functions are some of the most amazing objects in mathematics. They have been studied by Riemann, Picard, Kovalevski, Frobenious among many others.
We focus on theta functions of algebraic curves, and more explicitly on theta-nulls of superelliptic curves.
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Genus 3 curves
Genus 3 curves are ternary quartics. If the curve is hyperelliptic then they are written as
where f(x) is a polynomial of degree 8.
Genus 3 hyperelliptic curves are treated in the package of hyperelliptic curves.
Here we deal with non-hyperelliptic genus 3 curves. The most famous of them all is perhaps the Klein's quartic.
AMS Special Session: March 2012, Tampa, Florida.
Conferences and Activities
Algebraic Geometry Blog
Equation of curves over their field of definition
Let C be a curve defined over the complex numbers and F its field of definition. Finding a curve $X$, isomorphic to C over the complex numbers, is an old problem in algebraic geometry.
Algorithms exist for genus 2 curves due to work of Clebsch, Mestre, Shaska, Cardona, et al. We focus on genus 3 curves and on superelliptic curves of any genus.
More information can be found here.