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Preface

Introduction

Prologue: Warming up with Cross Ratios, and the Definition of Moduli Space / 0：

Cross ratios / 0.1：

Definition of moduli space / 0.2：

Stable n-pointed Curves / 1：

n-pointed smooth rational curves / 1.1：

Stable n-pointed rational curves / 1.2：

Stabilization, forgetting marks, contraction / 1.3：

Sketch of the construction of [Characters not reproducible subscript 0,n] / 1.4：

The boundary / 1.5：

Generalizations and references / 1.6：

Stable Maps / 2：

Maps P[superscript 1 Characters not reproducible] P[superscript r] / 2.1：

1-parameter families / 2.2：

Kontsevich stable maps / 2.3：

Idea of the construction of [Characters not reproducible subscript 0,n] (P[superscript r], d) / 2.4：

Evaluation maps / 2.5：

Forgetful maps / 2.6：

Easy properties and examples / 2.7：

Complete conics / 2.9：

Enumerative Geometry via Stable Maps / 2.10：

Classical enumerative geometry / 3.1：

Counting conics and rational cubics via stable maps / 3.2：

Kontsevich's formula / 3.3：

Transversality and enumerative significance / 3.4：

Stable maps versus rational curves / 3.5：

Gromov-Witten Invariants / 3.6：

Definition and enumerative interpretation / 4.1：

Properties of Gromov-Witten invariants / 4.2：

Recursion / 4.3：

The reconstruction theorem / 4.4：

Quantum Cohomology / 4.5：

Quick primer on generating functions / 5.1：

The Gromov-Witten potential and the quantum product / 5.2：

Associativity / 5.3：

Kontsevich's formula via quantum cohomology / 5.4：

Bibliography / 5.5：

Index

Preface

Introduction

Prologue: Warming up with Cross Ratios, and the Definition of Moduli Space / 0：

目次情報: 続きを見る

Preface

Tangent Variation Principle

Satellite Principles

Modification of Length-area Principle

Estimates for collections of Gamma-Lines

Estimates of lengths of Gamma-Lines for angular-quasiconformal mappings

Remarks on applying of estimates of L (D, Gamma)

Nevanlinna and Ahilfors Theories

Additions

Basic concepts and outcomes of Nevanlinna Value Distribution theory and Ahlfors theory of covering surfaces

Geometric deficient values

On some

Preface

Tangent Variation Principle

Satellite Principles

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