(An) Introductory Study on Toric Varieties

Abstract

This thesis provides a self-contained introduction to the theory of Toric Varieties. We discuss the face structures of a convex polyhedral cone, and then define toric varieties from ``fans``. Invariant toric subvarieties under the torus action give insight of the inner structure of a toric variety. Toric morphisms, especially blowups and blowdowns provide powerful tools to transfer regular, complete toric varieties, which also help resolve singularities. Finally we establish the equivalence between completeness and compactness of a toric variety.