Study on enumerative geometry and stable maps

Abstract

The primary aim of this thesis is to introduce the relations among the moduli space of stable maps, the Gromov-Witten invariants and enumerative geometry. In this thesis, we will see how the Gromov-Witten invariants give the solutions of the enumerative geometry problems. Especially, we focus on the multiplication table of the quantum cohomology ring which gives nontrivial relations among the enumerative solutions.