Supersingular abelian varieties and curves, and their moduli spaces, with a remark on the dimension of the moduli of supersingular curves of genus 4 (Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties)

Abstract

We give a survey on fundamentals of supersingular abelian varieties and supersingular curves and their moduli spaces. As an application of the explicit description of supersingular locus in the low dimensional case, we obtain a new result on the dimension of some components of the moduli space of supersingular curves of genus 4.