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 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 …

We consider the possibility of breaking the GUT group to the Standard Model gauge group
in F-theory compactifications by turning on certain U(1) fluxes. We show that the requirement …

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 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 …

1.1. Moduli spaces of Abelian and quadratic differentials.—The moduli space Hg of pairs (C,
ω) where C is a smooth complex curve of genus g and ω is an Abelian differential (or, in the …

In this paper, we derive the main properties of Kähler fibrations. We introduce the associated
Levi-Civita superconnection to construct analytic torsion forms for holomorphic direct …

We describe in mathematical detail the Nahm transformation which maps anti-self dual
connections on the four-torus (S 1) 4 onto anti-self-dual connections on the dual torus. This …

The purpose of this paper is to establish an asymptotic fomula for the Ray-Singer analytic
torsion associated with increasing powers of a given positive line bundle. Let Mbe a …

We study the generating functional, the adiabatic curvature and the adiabatic phase for the
integer quantum Hall effect (QHE) on a compact Riemann surface. For the generating …