Dan Coman (Syracuse University): Restricted spaces of holomorphic sections vanishing along subvarieties

Joi, 14 martie, ora 16, vă invităm să participați la următoarea prelegere invitată susținută în cadrul colectivului de Geometrie:

Restricted spaces of holomorphic sections vanishing along subvarieties

susținută de Dan Coman (Syracuse University).

Prelegerea va avea loc online, folosind Microsoft Teams la acest link de acces.

Abstract: Let L be a holomorphic line bundle on a compact normal complex space X of dimension n, let Σ = (Σ1,…,Σl) be an l-tuple of distinct irreducible proper analytic subsets of X, and τ = (τ1,…,τl) be an l-tuple of positive real numbers. We consider the space H00(X,Lp) of global holomorphic sections of Lp := Lp that vanish to order at least τjp along Σj, 1 ≤ jl, and give necessary and sufficient conditions to ensure that dim H00(X,Lp) ∼ pn. If YX is an irreducible analytic subset of dimension m, we also consider the space H00(X|Y,Lp) of holomorphic sections of Lp|Y that extend to global holomorphic sections in H00(X,Lp), and we give a general condition on Y to ensure that dim H00(X|Y,Lp) ∼ pm. When L is endowed with a continuous Hermitian metric, we show that the Fubini-Study currents of the spaces H00(X|Y,Lp) converge to a certain equilibrium current on Y, and we apply this to the study of the equidistribution of zeros in Y of random holomorphic sections in H00(X|Y,Lp) as p → ∞. This is joint work with George Marinescu and Viêt-Anh Nguyên.