Pushforwards of Measures on Real Varieties under Maps with Rational SingularitiesPublic Deposited
Let X,Y be algebraic varieties defined over the reals. Assume Y is smooth and X is Gorenstein. Suppose f:X -> Y is a flat R-morphism such that all the fibers have rational singularities. We show that the pushforward of any smooth, compactly supported measure on X has a continuous density with respect to any smooth measure with non-vanishing density on Y. This extends a result of Aizenbud and Avni from the p-adic case to the archimedean case.