Related papers: Torsors and stable equivariant birational geometry

We introduce equivariant Burnside groups, new invariants in equivariant birational geometry, generalizing birational symbols groups for actions of finite abelian groups, due to Kontsevich, Pestun, and the second author, and study their…

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

We propose new invariants in equivariant birational geometry, combining equivariant intermediate Jacobians and the Burnside formalism, for smooth rationally connected threefolds with actions of finite groups.

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

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

We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups.

We construct new invariants of equivariant birational isomorphisms taking values in equivariant Burnside groups.

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 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 linearizability and stable linearizability of actions of finite groups on the Segre cubic and Burkhardt quartic, using techniques from group cohomology, birational rigidity, and the Burnside formalism.

Torus orbifolds are topological generalization of symplectic toric orbifolds. We give a construction of smooth orbifolds with torus actions whose boundary is a disjoint union of torus orbifolds using toric topological method. As a result,…

We complete the classification of regular generically free actions of finite groups on del Pezzo surfaces, up to birational equivalence. As a byproduct, we settle several open problems in equivariant birational geometry, e.g., we classify…

In this paper we will survey some recent developments in the last decade or so on variation of Geometric Invariant Theory and its applications to Birational Geometry such as the weak Factorization Theorems of nonsingular projective…

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

We restrict geometric tangential equivariant complex $T^n$-bordism to torus manifolds and provide a complete combinatorial description of the appropriate non-commutative ring. We discover, using equivariant $K$-theory characteristic…

We discuss invariants in equivariant birational geometry.

We construct and study universal spaces for birational invariants of algebraic varieties over algebraic closures of finite fields.

We study the equations of universal torsors on rational surfaces.

This text gives some results about quantum torsors. Our starting point is an old reformulation of torsors recalled recently by Kontsevich. We propose an unification of the definitions of torsors in algebraic geometry and in Poisson…