A higher-dimensional generalization of Mumford's rational pullback for Weil divisors

TL;DR

This paper extends Mumford's rational pullback concept from normal surfaces to certain higher-dimensional cases, establishing its existence and properties despite the complexities of higher dimensions.

Contribution

It identifies a specific higher-dimensional setting where a Mumford-like rational pullback for Weil divisors can be defined with key properties.

Findings

Existence of a rational pullback in the identified higher-dimensional setting

The pullback is linear and respects effectivity

The pullback satisfies the projection formula

Abstract

Mumford defined a rational pullback for Weil divisors on normal surfaces, which is linear, respects effectivity, and satisfies the projection formula. In higher dimensions, the existence of small resolutions of singularities precludes such general results. We single out a higher-dimensional situation that resembles the surface case and show for it that a rational pullback for Weil divisors exists, which is also linear, respects effectivity, and satisfies the projection formula.