相关论文: Intersection forms, topology of maps and motivic d…

We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij-S\"oderberg theory. That is, given a Betti diagram, we determine if it is possible to decompose it into the Betti diagrams of complete…

We prove a deletion-contraction formula for motivic Feynman rules given by the classes of the affine graph hypersurface complement in the Grothendieck ring of varieties. We derive explicit recursions and generating series for these motivic…

In this paper we define the triangulated category of motives over a simplicial scheme. The morphisms between the Tate objects in this category compute the motivic cohomology of the underlying scheme. In the last section we consider the…

Grothendieck-Chow motives of quadric hypersurfaces have provided many insights into the theory of quadratic forms. Subsequently, the landscape of motives of more general projective homogeneous varieties has begun to emerge. In particular,…

In this work we develop a theory of motives for logarithmic schemes over fields in the sense of Fontaine, Illusie, and Kato. Our construction is based on the notion of finite log correspondences, the dividing Nisnevich topology on log…

The perverse filtration in cohomology and in cohomology with compact supports is interpreted in terms of kernels of restrictions maps to suitable subvarieties by using the Lefschetz hyperplane theorem and spectral objects. Various…

The isometry class of the intersection form of a compact complex surface can be easily determined from complex-analytic invariants. For projective surfaces the primitive lattice is another naturally occurring lattice. The goal of this note…

These notes aim to give a first introduction to intersection cohomology and perverse sheaves with applications to representation theory or quantum groups in mind.

For a split reductive group G over a finite field, we show that the intersection (cohomology) motive of the moduli stack of iterated G-shtukas with bounded modification and level structure is defined independently of the standard…

Given a perversity function in the sense of intersection homology theory, the method of intersection spaces assigns to certain oriented stratified spaces cell complexes whose ordinary reduced homology with real coefficients satisfies…

The purpose of this paper is to introduce a version of singular homology based on smooth mappings of manifolds with corners. Although variants of such a theory exists in the literature, we felt that certain points were not adequately…

We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij--Soederberg theory. That is, given a Betti diagram, we decompose it into pure diagrams. Relaxing the requirement that the degree sequences…

We provide a generalization of the Deligne sheaf construction of intersection homology theory, and a corresponding generalization of Poincar\'e duality on pseudomanifolds, such that the Goresky-MacPherson, Goresky-Siegel, and…

In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite…

This note addresses the motivic nature of some classical cohomological results due to Lefschetz, namely the primitive decomposition (for the cohomology of smooth projective varieties), and, secondly, the splitting of the cohomology of a…

Sawin recently gave an axiomatic characterization of multiple Dirichlet series over the function field $\mathbb{F}_{q}(T)$ and proved their existence by exhibiting the coefficients as trace functions of specific perverse sheaves. However,…

This is the announcement, and the long summary, of a series of articles on the algorithmic study of Thurston maps. We describe branched coverings of the sphere in terms of group-theoretical objects called bisets, and develop a theory of…

The aim of this monograph is twofold: to explain various nonautonomous integrable systems (discrete Painlev\'e all the way up to the elliptic level, as well as generalizations \`a la Garnier) using an interpretation of difference and…

The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…

We prove that a standard realization of the direct image complex via the so-called Douady-Barlet morphism associated with a smooth complex analytic surface admits a natural decomposition in the form of an injective quasi-isomorphism of…