The main purpose of this paper is to prove a general result about the geometry of
holomorphic line bundles over Kähler manifolds. This result is essentially a partial …

We study the near diagonal asymptotic expansion of the generalized Bergman kernel of the
renormalized Bochner-Laplacian on high tensor powers of a positive line bundle over a …

We show, using a direct variational approach, that the second boundary value problem for
the Monge-Ampere equation in Rn with exponential non-linearity and target a convex body …

Abstract We study the Berezin-Toeplitz quantization on symplectic manifolds making use of
the full off-diagonal asymptotic expansion of the Bergman kernel. We give also a …

We study BerezinToeplitz quantization on Khler manifolds. We explain first how to compute
various associated asymptotic expansions, then we compute explicitly the first terms of the …

We show that the variance of the number of simultaneous zeros of m iid Gaussian random
polynomials of degree N in an open set U ⊂ C^ m with smooth boundary is asymptotic to N …

In this paper we study the asymptotic behaviour of the spectral function corresponding to the
lower part of the spectrum of the Kodaira Laplacian on high tensor powers of a holomorphic …

We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line
bundle under hypotheses of bounded geometry. Further, we give Bergman kernel proofs of …

Using log canonical thresholds and basis divisors Fujita–Odaka introduced purely algebro-
geometric invariants δ m whose limit in m is now known to characterize uniform K-stability on …

In this paper we consider a punctured Riemann surface endowed with a Hermitian metric
that equals the Poincaré metric near the punctures, and a holomorphic line bundle that …