Search results for "14E08"
showing 3 items of 3 documents
Rationalizability of square roots
2020
Feynman integral computations in theoretical high energy particle physics frequently involve square roots in the kinematic variables. Physicists often want to solve Feynman integrals in terms of multiple polylogarithms. One way to obtain a solution in terms of these functions is to rationalize all occurring square roots by a suitable variable change. In this paper, we give a rigorous definition of rationalizability for square roots of ratios of polynomials. We show that the problem of deciding whether a single square root is rationalizable can be reformulated in geometrical terms. Using this approach, we give easy criteria to decide rationalizability in most cases of square roots in one and…
Symmetric locally free resolutions and rationality problems
2022
We show that the birationality class of a quadric surface bundle over $\mathbb{P}^2$ is determined by its associated cokernel sheaves. As an application, we discuss stable-rationality of very general quadric bundles over $\mathbb{P}^2$ with discriminant curves of fixed degree. In particular, we construct explicit models of these bundles for some discriminant data. Among others, we obtain various birational models of a nodal Gushel-Mukai fourfold, as well as of a cubic fourfold containing a plane. Finally, we prove stable irrationality of several types of quadric surface bundles.
The Tautological Ring of Spin Moduli Spaces
2009
We introduce the notion of tautological ring for the moduli space of spin curves. Moreover, we study some relations among tautological classes which are motivated by physics. Finally, we show that the Chow rings of these moduli spaces are tautological in low genus.