NEW EXAMPLES OF HYPERKÄHLER MANIFOLDS

By MARY MARTINEZ

CONTENTS PART I HYPERHOLOMORPHIC SHEAVES AND NEW EXAMPLES OF HYPERKÄHLER MANIFOLDS 1 INTRODUCTION 2 HYPERKÄHLER MANIFOLDS 3 HYPERHOLOMORPHIC SHEAVES 4 COHOMOLOGY OF HYPERKÄHLER MANIFOLDS 5 C-RESTRICTED COMPLEX STRUCTURES ON HYPERKÄHLER MANIFOLDS 6 DESINGULARIZATION OF HYPERHOLOMORPHIC SHEAVES 7 TWISTOR TRANSFORM AND QUATERNIONIC-KÄHLER GEOMETRY 8 C*-EQUIVARIANT TWISTOR SPACES 9 MODULI SPACES OF HYPERHOLOMORPHIC SHEAVES AND BUNDLES 10 NEW EXAMPLES OF HYPERKÄHLER MANIFOLDS PART II HYPERKÄHLER STRUCTURES ON TOTAL SPACES OF HOLOMORPHIC COTANGENT BUNDLES 1 PRELIMINARY FACTS FROM LINEAR ALGEBRA 2 HODGE BUNDLES AND QUATERNIONIC MANIFOLDS 3 HODGE MANIFOLDS 4 REGULAR HODGE MANIFOLDS 5 TANGENT BUNDLES AS HODGE MANIFOLDS 6 FORMAL COMPLETIONS 7 PRELIMINARIES ON THE WEIL ALGEBRA 8 CLASSIFICATION OF FLAT EXTENDED CONNECTIONS 9 METRICS 10 CONVERGENCE