Dan Coman (Syracuse University): Restricted spaces of holomorphic sections vanishing along subvarieties
Am Donnerstag, dem 14. März, um 16 Uhr, laden wir Sie zur folgenden Gastvorlesung ein, die innerhalb der Geometrie-Gruppe vorgestellt wird:
Restricted spaces of holomorphic sections vanishing along subvarieties
vorgetragen von Dan Coman von Syracuse University.
Der Vortrag wird live auf Microsoft Teams abgehalten (Link).
Abstract: Let L be a holomorphic line bundle on a compact normal complex space X of dimension n , let Σ = ( Σ 1 ,…, Σ l ) be an l -tuple of distinct irreducible proper analytic subsets of X , and τ = ( τ 1 ,…, τ l ) be an l -tuple of positive real numbers. We consider the space H 0 0 ( X , L p ) of global holomorphic sections of L p := L ⊗ p that vanish to order at least τ j p along Σ j , 1 ≤ j ≤ l , and give necessary and sufficient conditions to ensure that dim H 0 0 ( X , L p ) ∼ p n . If Y ⊂ X is an irreducible analytic subset of dimension m , we also consider the space H 0 0 ( X | Y , L p ) of holomorphic sections of L p | Y that extend to global holomorphic sections in H 0 0 ( X , L p ) , and we give a general condition on Y to ensure that dim H 0 0 ( 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 H 0 0 ( 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 H 0 0 ( X | Y , L p ) as p → ∞. This is joint work with George Marinescu and Viêt-Anh Nguyên.
