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Coman, Dan, Marinescu, George ORCID: 0000-0001-6539-7860 and Nguyên, Viêt-Anh (2025). Restricted spaces of holomorphic sections vanishing along subvarieties. Mathematische Zeitschrift, 310 (1). Springer Nature. ISSN 0025-5874

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Abstract

[Artikel-Nr. 9] Let X be a compact normal complex space of dimension n and L be a holomorphic line bundle on X. Suppose that Σ = ( Σ 1 , … , Σ ℓ ) is an ℓ -tuple of distinct irreducible proper analytic subsets of X , τ = ( τ 1 , … , τ ℓ ) is an ℓ -tuple of positive real numbers, and let H 0 0 ( X , L p ) be the space of holomorphic sections of L p : = L ⊗ p that vanish to order at least τ j p along Σ j , 1 ≤ j ≤ ℓ. If Y ⊂ X is an irreducible analytic subset of dimension m , we 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). Assuming that the triplet (L, Σ, τ) is big in the sense that dim H 0 0 (X, L p) ∼ p n , 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. 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 → ∞.

Item Type:	Article
Creators:	Creators Email ORCID ORCID Put Code Coman, Dan UNSPECIFIED UNSPECIFIED UNSPECIFIED Marinescu, George UNSPECIFIED https://orcid.org/0000-0001-6539-7860 UNSPECIFIED Nguyên, Viêt-Anh UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-797042
Identification Number:	10.1007/s00209-025-03706-w
Journal or Publication Title:	Mathematische Zeitschrift
Volume:	310
Number:	1
Date:	17 May 2025
Publisher:	Springer Nature
ISSN:	0025-5874
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	Mathematics
['eprint_fieldname_oa_funders' not defined]:	Publikationsfonds UzK
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/79704