31. However the correction to the metric of the moduli space of vacua from instantons was calculated in a series of papers. 32. More conceptually, modular functions can be thought of as functions on the moduli space of isomorphism classes of complex elliptic curves. 33. Borcherds used this theory to resolve some long-standing conjectures concerning quasi-affineness of certain moduli spaces of algebraic surfaces. 34. Eventually, in genus zero the coarse moduli space has dimension zero, and in genus one, it has dimension one. 35. Moreover, natural considerations regarding, for example, moduli spaces , lead to schemes that are " non-classical ". 36. The moduli space of stable maps is compact; that is, any sequence of stable maps converges to a stable map. 37. Thus they form a natural higher-dimensional generalization of modular curves viewed as moduli spaces of elliptic curves with level structure. 38. His major contributions are in theory of classical and quantum integrable systems, quantum groups and Weil Petersson geometry of moduli spaces . 39. This moduli space is the essence of the Gromov Witten invariants, which find application in enumerative geometry and type IIA string theory. 40. More precisely, the existence of non-trivial automorphisms of the objects being classified makes it impossible to have a fine moduli space .
