Related papers: Equivariant unirationality of tori in small dimens…

We study unirationality of actions of finite groups on Fano threefolds.

We study linear actions of finite groups in small dimensions, up to equivariant birationality.

We introduce a torsor-theoretic obstruction to equivariant unirationality and show that it is also sufficient for actions of finite groups on toric varieties arising from automorphisms of the torus.

We study cohomological obstructions to equivariant unirationality, with special regard to actions of finite groups on del Pezzo surfaces and Fano threefolds.

We develop the formalism of universal torsors in equivariant birational geometry and apply it to produce new examples of nonbirational but stably birational actions of finite groups.

A new proof of equivariant resolution of singularities under a finite group action in characteristic 0 is provided. We assume we know how to resolve singularities without group action. We first prove equivariant resolution of toroidal…

We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.

We study the equivariant cobordism theory of schemes for action of linear algebraic groups. We compare the equivariant cobordism theory for the action of a linear algebraic groups with similar groups for the action of tori and deduce some…

We provide new stable linearizability constructions for regular actions of finite groups on homogeneous spaces and low-dimensional quadrics.

We study $G$-equivariant birational geometry of toric varieties, where $G$ is a finite group.

We study linearizability of actions of finite groups on cubic threefolds with non-isolated singularities.

We describe complete simplicial toric varieties on which a unipotent group acts with a finite number of orbits. We also provide a complete list of such varieties in the case where the dimension is equal to 2.

Fix a finite group $G$. We seek to classify varieties with $G$-action equivariantly birational to a representation of $G$ on affine or projective space. Our focus is odd-dimensional smooth complete intersections of two quadrics, relating…

We prove scale-invariant Strichartz inequalities for the Schrodinger equation on rectangular tori (rational or irrational) in all dimensions. We use these estimates to give a unified and simpler treatment of local well-posedness of the…

We introduce and study some families of groups whose irreducible characters take values on quadratic extensions of the rationals. We focus mostly on a generalization of inverse semi-rational groups, which we call uniformly semi-rational…

We prove a Grothendieck-Lefschetz theorem for equivariant Picard groups of non-singular varieties with finite group actions.

We introduce tropically unirational varieties, which are subvarieties of tori that admit dominant rational maps whose tropicalisation is surjective. The central (and unresolved) question is whether all unirational varieties are tropically…

We apply the equivariant Burnside group formalism to distinguish linear actions of finite groups, up to equivariant birationality. Our approach is based on De Concini-Procesi models of subspace arrangements.

We discuss the equivariant Burnside group and related new invariants in equivariant birational geometry, with a special emphasis on applications in low dimensions.

Equivariant Riemann-Roch theorem for the complex variety under the action of complex linear reductive algebraic group.