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Equidistribution for weakly holomorphic sections of line bundles on algebraic curves
Dan Coman1; George Marinescu2
1 Department of Mathematics, Syracuse University, Syracuse, NY 13244-1150, USA
2 Univerisität zu Köln, Mathematisches institut, Weyertal 86-90, 50931 Köln, Germany and Institute of Mathematics “Simion Stoilow”, Romanian Academy, Bucharest, Romania
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 31 (2022) no. 3, pp. 949-973.

We prove the convergence of the normalized Fubini–Study measures and the logarithms of the Bergman kernels of various Bergman spaces of holomorphic and weakly holomorphic sections associated to a singular Hermitian holomorphic line bundle on an algebraic curve. Using this, we study the asymptotic distribution of the zeros of random sequences of sections in these spaces.

Nous prouvons la convergence des mesures de Fubini–Study normalisées et des logarithmes des noyaux de Bergman de certains espaces de Bergman de sections holomorphes et faiblement holomorphes associées à un fibré holomorphe hermitien singulier sur une courbe algébrique. A l’aide de ce résultat, nous étudions la distribution asymptotique des zéros de suites aléatoires de sections dans ces espaces.

Published online:
DOI: 10.5802/afst.1709
Classification: 32L10, 14H60, 30F10, 32U40
Keywords: Bergman kernel, Fubini–Study current, singular Hermitian metric, algebraic curve, weakly holomorphic sections

Dan Coman 1; George Marinescu 2

1 Department of Mathematics, Syracuse University, Syracuse, NY 13244-1150, USA
2 Univerisität zu Köln, Mathematisches institut, Weyertal 86-90, 50931 Köln, Germany and Institute of Mathematics “Simion Stoilow”, Romanian Academy, Bucharest, Romania
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Dan Coman; George Marinescu. Equidistribution for weakly holomorphic sections of line bundles on algebraic curves. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 31 (2022) no. 3, pp. 949-973. doi : 10.5802/afst.1709. https://afst.centre-mersenne.org/articles/10.5802/afst.1709/

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