Parameter spaces: constructions and examples * Basic facts about moduli spaces of curves * Techniques * Construction of M_g * Limit Linear Series and the Brill-Noether Theory * Geometry of moduli spaces: Selected Results.

Moduli of curves

Mirror symmetry for lattice polarizedK3 surfaces

These are expository lectures reviewing (1) recent developments in two-dimensional YangMills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinite-dimensional differential geometry. We emphasize the unifying role of equivariant cohomology both as the underlying principle in the formulation of BRST transformation laws and as a central concept in the geometrical interpretation of topological field theory path integrals.

Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories

K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.

Lectures on K3 Surfaces

Enriques Surfaces I

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On Deformations of Quintic Surfaces.

/pdf/on-deformations-of-holomorphic-maps-i-22hzxz07hx.pdf

On deformations of holomorphic maps I

/pdf/on-the-periods-of-enriques-surfaces-i-2c0gy7i40q.pdf

On the Periods of Enriques Surfaces. I.

/pdf/on-the-periods-of-enriques-surfaces-i-18gwclwagh.pdf

Eiji Horikawa

Papers

On Deformations of Quintic Surfaces.

On deformations of holomorphic maps I

On the Periods of Enriques Surfaces. I.

On the Periods of Enriques Surfaces. I

On deformations of holomorphic maps. III