TY - JOUR
T1 - Convergence of fubini-study currents for orbifold line bundles
AU - Coman, Dan
AU - Marinescu, George
N1 - Funding Information:
Dan Coman is grateful to the Alexander von Humboldt Foundation for their support and to the Mathematics Institute at the University of Köln for their hospitality.
Funding Information:
The first author was partially supported by the NSF Grant DMS-1300157 and the second author was partially supported by SFB TR 12.
PY - 2013/6
Y1 - 2013/6
N2 - We discuss positive closed currents and Fubini-Study currents on orbifolds, as well as Bergman kernels of singular Hermitian orbifold line bundles. We prove that the Fubini-Study currents associated to high powers of a semipositive singular line bundle converge weakly to the curvature current on the set where the curvature is strictly positive, generalizing a well-known theorem of Tian. We include applications to the asymptotic distribution of zeros of random holomorphic sections.
AB - We discuss positive closed currents and Fubini-Study currents on orbifolds, as well as Bergman kernels of singular Hermitian orbifold line bundles. We prove that the Fubini-Study currents associated to high powers of a semipositive singular line bundle converge weakly to the curvature current on the set where the curvature is strictly positive, generalizing a well-known theorem of Tian. We include applications to the asymptotic distribution of zeros of random holomorphic sections.
KW - Bergman kernel
KW - Fubini-Study current
KW - Orbifolds and orbifold line bundles
KW - equidistribution of zeros
KW - random holomorphic section
KW - singular Hermitian metric
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U2 - 10.1142/S0129167X13500511
DO - 10.1142/S0129167X13500511
M3 - Article
AN - SCOPUS:84880980995
VL - 24
JO - International Journal of Mathematics
JF - International Journal of Mathematics
SN - 0129-167X
IS - 7
M1 - 1350051
ER -