Number of Moduli of Families of Curves on Toric Surfaces

摘要

An algebraic torus T of dimension n is an algebraic group isomorphic to (C*)(sup n), where n is = or > 1. A toric variety is a variety which contains a n-dimensional algebraic torus T as an open subvariety and such that the action of T on itself extends to an action on the whole variety. The easiest examples are C(sup n) and P(sup n). Topics discussed in the thesis include: Toric varieties--definitions and invariants; Families of curves on a toric surface; Properties of curves on a toric surface; Classification of polygons; The ideal of a projective embedded toric variety.