The Moduli Space of Curves (Progress in Mathematics) etc. - kelloggchurch.org

# Moduli of algebraic curves - Wikipedia.

elliptic curves over Ki.e. the equation de ning the curve has coe cients in K up to isomorphism. We consider curves E 1;E 2 over Kto be isomorphic if there is a map ’: E 1!E 2 de ned over K meaning the coe cients of ’are in K. This is an example of a moduli problem. We begin by studying EllC. Elliptic curves over C have a particularly. Basic concepts in moduli theory. Let $S$ be a scheme a complex or algebraic space. A family of objects parametrized by the scheme $S$ or, as is often said, "scheme over Sover S" or "scheme with basis Swith basis S" is a set of objects$$\ X _s: s \in S, X _s \in A \,$$ equipped with an additional structure compatible with the structure of the base $S$. Jul 07, 2014 · J. Harris, D. Mumford, "On the Kodaira dimension of the moduli space of curves" Invent. Math., 67 1982 pp. 23–86 MR0664324 Zbl 0506.14016 [a4] S. Mori, S. Mukai, "Uniruledness of the moduli space of curves of genus 11" M. Reynard ed. T. Shioda ed., Algebraic geometry, Lect. notes in math., 1016, Springer 1983 pp. 334–353 MR0726433.