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19942026
most citedGerms of arcs on singular algebraic varieties and motivic integration

209 citations

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107 papers · 1 filter

math.AG2026

Moderate and rapid-decay nearby cycles for holonomic D-modules

Claude Sabbah

We introduce the notion of moderate and rapid decay nearby cycles relative to a holomorphic function for an arbitrary holonomic -module. They are proved to be $\ma…

math.AG2026

An atomic criterion for irrationality without quantum computations

Vladimiro Benedetti, Aideen Fay, Jérémy Guéré +2

The birational invariants introduced by Katzarkov-Kontsevich-Pantev-Yu allows one to obtain irrationality results for varieties whose quantum cohomology is well-behaved. We observe…

math.AG2026

Quantum cohomology and irrationality of Gushel-Mukai fourfolds

Vladimiro Benedetti, Laurent Manivel, Nicolas Perrin

We compute the small quantum cohomology of Gushel-Mukai fourfolds. Following [13], our computations imply that the very general ones are not rational. Following [8], and thanks to…

math.AG2025

The Deligne-Riemann-Roch isomorphism

Dennis Eriksson, Gerard Freixas i Montplet

This work establishes the geometric component of Deligne's longstanding program on refined Grothendieck-Riemann-Roch formulas expressed through determinants of cohomology. The appr…

math.AG2025

Three results on holonomic D-modules

Claude Sabbah

In this text, we illustrate the use of local methods in the theory of (irregular) holonomic D-modules. I. (The Euler characteristic of the de~Rham complex) We show the invariance o…

math.AG2025

Equality of tropical rank and dimension for semimodules of tropical rational functions, and computational aspects

Omid Amini, Stéphane Gaubert, Lucas Gierczak

The tropical rank of a semimodule of rational functions on a metric graph mirrors the concept of rank in linear algebra. Defined in terms of the maximal number of tropically indepe…