Asymptotics of partial density function vanishing along smooth subvariety

Abstract

We study the asymptotic of the partial density function associated to holomorphic section of a postive line bundle vanishing to high orders along a fixed smooth subvariety. Assuming local torus-action-invariance, we describe the forbidden region, generalizing the result of Ross-Singer.

References in corpus (8)

• Distribution of zeros of random and quantum chaotic sections of positive line bundles
• Universality and scaling of correlations between zeros on complex manifolds
• Critical points and supersymmetric vacua
• Poincare-Lelong approach to universality and scaling of correlations between zeros
• Correlations between zeros and supersymmetry
• Bergman kernels and equilibrium measures for ample line bundles
• Interface asymptotics of partial Bergman kernels on $S^1$-symmetric Kaehler manifolds
• Estimations of the Bergman kernel of the punctured disk