From the 1 of 8 linked papers with an AI index.
8 papers
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…
Sphericality of spaces of conics on homogeneous spaces
Minseong Kwon, Nicolas Perrin
We prove that the Hilbert scheme of conics on , a projective rational homogeneous space with Picard rank one, is -spherical if and only if is associated to a long r…
Quantum cohomology and birational geometry of Verra fourfolds
Vladimiro Benedetti, Jérémy Guéré, Laurent Manivel +1
We compute the small quantum cohomology ring of a Verra fourfold. Using the theory of atoms recently developped by Katzarkov--Kontsevich--Pantev--Yu, and building on recent papers…
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…
Seidel and Pieri products in cominuscule quantum K-theory
Anders S. Buch, Pierre-Emmanuel Chaput, Nicolas Perrin
We prove a collection of formulas for products of Schubert classes in the quantum -theory ring of a cominuscule flag variety . This includes a -theory version of t…
Positivity of minuscule quantum K-theory
Anders S. Buch, Pierre-Emmanuel Chaput, Leonardo C. Mihalcea +1
We prove that the Schubert structure constants of the quantum -theory ring of any minuscule flag variety or quadric hypersurface have signs that alternate with codimension. We a…