Mathematics

Moduli of algebraic curves are of classical interest. Statedin terms of functors, the problem boils down to the question of repre-sentability of the moduli functor by a scheme and existence of a universalfamily over the said scheme. Existence of non-trivial automorphisms foralgebraic curves implies that such moduli problems cannot be solved in thesetting of schemes. Historically, attempts to find a reasonable geometricsolution to this moduli problem led to the notion of stack. I will attemptto show the problems with the classical theory and give a flavor of howstacks provide a resolution, using, as an example, the moduli of ellipticcurves.