The study of Kahler-Einstein metrics was pioneered by E. Calabi more than forty years ago.
In the mid-70's, Yau's celebrated solution of the Calabi conjecture opened a new chapter …

The first edition of this book presented simple proofs of the Atiyah-Singer Index Theorem for
Dirac operators on compact Riemannian manifolds and its generalizations (due to the …

This book treats the Atiyah-Singer index theorem using the heat equation, which gives a
local formula for the index of any elliptic complex. Heat equation methods are also used to …

This thorough and detailed exposition is the result of an intensive month-long course on
mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry …

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 …

We attach secondary invariants to any acyclic complex of holomorphic Hermitian vector
bundles on a complex manifold. These were first introduced by Bott and Chern [Bot C]. Our …

Let i: Y—> X be an embedding of compact complex manifolds. Let r| be a holomorphic vector
bundle on Y and let (0.1)(^): o^-^ _,...-^-. 0 vv be a holomorphic chain complex of vector …

There is the general principle to consider a classical invariant of a closed Riemannian
manifold M and to define its analog for the universal covering M taking the action of the …

We prove in this paper an arithmetic analog of the Riemann-Roch-Grothendieck theorem for
the determinant of the cohomology of an Hermitian vector bundle of arbitrary rank on a …

We consider holomorphic Poisson-BF theory on twistor space. Classically, this describes
self-dual Einstein gravity on space-time, but at the quantum level it is plagued by an …