Pushforwards of Measures on Real Varieties under Maps with Rational Singularities

Andrew Reiser

Pushforwards of Measures on Real Varieties under Maps with Rational Singularities

Algebraic Geometry 2018-07-03 v1

Authors: Andrew Reiser

Abstract

Let $X,Y$ be algebraic varieties defined over $\Bbb R$ . Assume $Y$ is smooth and $X$ is Gorenstein. Suppose $\varphi:X\to Y$ is a flat $\Bbb R$ -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.

Keywords

algebraic varieties rational singularities pushforward of measures continuous density archimedean case flat morphism

Cite

@article{arxiv.1807.00079,
  title  = {Pushforwards of Measures on Real Varieties under Maps with Rational Singularities},
  author = {Andrew Reiser},
  journal= {arXiv preprint arXiv:1807.00079},
  year   = {2018}
}

Comments

39 pages, no figures. arXiv admin note: text overlap with arXiv:1307.0371 by other authors

Pushforwards of Measures on Real Varieties under Maps with Rational Singularities

Abstract

Keywords

Cite

Comments

Related papers