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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…
An atomic criterion for irrationality without quantum computations
Vladimiro Benedetti, Aideen Fay, Jérémy Guéré +2
The paper presents a cohomological criterion that proves irrationality of certain algebraic varieties without computing quantum atoms, using monodromy equivariance and irreducibili…
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…
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…
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…