Pushforwards of Measures on Real Varieties under Maps with Rational Singularities
Andrew Reiser

TL;DR
This paper proves that under certain conditions, the pushforward of smooth measures on real algebraic varieties with rational singularities has a continuous density, extending previous p-adic results to the real case.
Contribution
It extends the known results about measure pushforwards with rational singularities from p-adic fields to real algebraic varieties.
Findings
Pushforward measures have continuous densities under specified conditions.
Extension of p-adic results to the archimedean (real) case.
Applicable to algebraic varieties with rational singularities.
Abstract
Let be algebraic varieties defined over . Assume is smooth and is Gorenstein. Suppose is a flat -morphism such that all the fibers have rational singularities. We show that the pushforward of any smooth, compactly supported measure on has a continuous density with respect to any smooth measure with non-vanishing density on . This extends a result of Aizenbud and Avni from the -adic case to the archimedean case.
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