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,…,Σ_l) be an l-tuple of distinct irreducible proper analytic subsets of X, and τ = (τ₁,…,τ_l) be an l-tuple of positive real numbers. We consider the space H₀⁰(X,L^p) of global holomorphic sections of L^p := L^⊗p that vanish to order at least τ_jp along Σ_j, 1 ≤ j ≤ l, and give necessary and sufficient conditions to ensure that dim H₀⁰(X,L^p) ∼ pⁿ. If Y ⊂ X is an irreducible analytic subset of dimension m, we also consider the space H₀⁰(X|Y,L^p) of holomorphic sections of L^p|Y that extend to global holomorphic sections in H₀⁰(X,L^p), and we give a general condition on Y to ensure that dim H₀⁰(X|Y,L^p) ∼ p^m. When L is endowed with a continuous Hermitian metric, we show that the Fubini-Study currents of the spaces H₀⁰(X|Y,L^p) 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,L^p) as p → ∞. This is joint work with George Marinescu and Viêt-Anh Nguyên.