This two volume work on Positivity in Algebraic Geometry contains a contemporary account
of a body of work in complex algebraic geometry loosely centered around the theme of …

The book starts with a thorough introduction to connections and holonomy groups, and to
Riemannian, complex and Kähler geometry. Then the Calabi conjecture is proved and used …

Riemannian geometry has today become a vast and important subject. This new book of
Marcel Berger sets out to introduce readers to most of the living topics of the field and …

This book examines holomorphic Morse inequalities and the asymptotic expansion of the
Bergman kernel on manifolds by using the heat kernel. It opens perspectives on several …

We use wall-crossing with respect to Bridgeland stability conditions to systematically study
the birational geometry of a moduli space MM of stable sheaves on a K3 surface XX:(a) We …

The goal of this work is to give a precise numerical description of the Kähler cone of a
compact Kähler manifold. Our main result states that the Kähler cone depends only on the …

We develop a theory of Bridgeland stability conditions and moduli spaces of semistable
objects for a family of varieties. Our approach is based on and generalizes previous work by …

This is an introduction to a very active field of research, on the boundary between
mathematics and physics. It is aimed at graduate students and researchers in geometry and …

This graduate level text covers an exciting and active area of research at the crossroads of
several different fields in Mathematics and Physics. In Mathematics it involves Differential …

This up-to-date introduction to Griffiths' theory of period maps and period domains focusses
on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation …