Lectures on Moduli Spaces of Elliptic Curves

Abstract

These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and stacks) important in the study of moduli spaces of curves and abelian varieties through the example of elliptic curves. The reason for working with elliptic curves is that most constructions are elementary and explicit in this case. All four approaches to moduli spaces of curves -- complex analytic, topological, algebro-geometric, and number theoretic -- are considered. Topics covered reflect my own biases. Very little, if anything, in these notes is original, except perhaps the selection of topics and the point of view.

typos corrected

Cited by in corpus (16)

• Notes on the Universal Elliptic KZB Equation
• On the algebraic structure of iterated integrals of quasimodular forms
• Duality group actions on fermions
• Generalized two-field $\alpha$-attractors from the hyperbolic triply-punctured sphere
• Categorical Equivalence and the Renormalization Group
• Special Lagrangian submanifolds of log Calabi-Yau manifolds
• Graphons, permutons and the Thoma simplex: three mod-Gaussian moduli spaces
• Dimension of the moduli space and Hamiltonian analysis of BF field theories
• On the global moduli of Calabi-Yau threefolds
• Multiple zeta values and iterated Eisenstein integrals
• Deligne-Beilinson Cohomology of Affine Groups
• Monodromy of Codimension-One Sub-Families of Universal Curves
• Equivariant triangulations of tori of compact Lie groups and hyperbolic extension to non-crystallographic Coxeter groups
• Global aspects of moduli spaces of 2d SCFTs
• Infinite Type D-modules and Higher Depth Mock Modular Forms I
• Tamely Ramified Covers of the Projective Line with Alternating and Symmetric Monodromy