Lelong numbers of currents of full mass intersection

Seshadri Constants via Lelong Numbers

One of Demailly’s characterizations of Seshadri constants on ample line bundles works with Lelong numbers of certain positive singular hermitian metrics. In this note sections of multiples of the line bundle are used to produce such metrics and then to deduce another formula for Seshadri constants. It is applied to compute Seshadri constants on blown up products of curves, to disprove a conject...

A Generalized Poincaré-lelong Formula and Explicit Green Currents

We prove the following generalization of the classical Poincaré-Lelong formula. Given a holomorphic section f , with zero set Z, of a Hermitian vector bundle E → X , let S be the line bundle over X \Z spanned by f and let Q = E/S. We prove that the Chern form c(DQ) is locally integrable and closed in X and that there is a current W such that ddW = c(DE)− c(DQ)− M, where M is a current with supp...

Heights, Currents, Intersection

These notes correspond to the ALGANT Graduate course given in Bordeaux during the academic year 2009-2010 (second semester). The course intends to be as self contained as possible. The notes (in French) of the graduate course Géométrie Différentielle Complexe (Niamey, December 2009), available on line at http://www.math.u-bordeaux1.fr/~yger/Cours-Niamey.pdf will help for some eventual perequisi...

Virtual Intersection Numbers

Intersection homology Betti numbers

A generalization of the formula of Fine and Rao for the ranks of the intersection homology groups of a complex algebraic variety is given. The proof uses geometric properties of intersection homology and mixed Hodge theory. The middle-perversity intersection homology with integral coefficients of a compact complex n-dimensional algebraic variety X with isolated singularities is well known to be...