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Asymptotics of Partial Density Functions for Divisors by Ross, Julius; Singer, Michael is a scholarly article available to read on EtoBox.

What is Asymptotics of Partial Density Functions for Divisors about?

We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor $Y$. Assuming the data in question is invariant under an $S^1$-action (locally around $Y$) we prove that this density function has a distributional asymptotic expansion that is in fact smooth upon passing to a suitable real blow-up. Moreover we recover the existence of the "forbidden region" $R$ on which the density function is exponentially small, and prove that it has an "error-function" behaviour across the boundary $\partial R$. As an illustrative application, we use this to study a certain natural function that can be associated to a divisor in a K\"ahler manifold.

Author

Ross, Julius; Singer, Michael

Published

2013

Language

EN