Related papers: Equivariant geometry of singular cubic threefolds

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

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

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 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 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.

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

We generalize the equivariant intermediate Jacobian torsor obstruction over $\mathbb{C}$ to algebraically closed fields of characteristic zero. It is an obstruction to the (projective) linearizability problem of finite group actions on…

We study equivariant deformations of singular curves with an action of a finite flat group scheme, using a simplified version of Illusie's equivariant cotangent complex. We apply these methods in a special case which is relevant for the…

We develop an equivariant version of the formalism of intermediate Jacobian torsor obstructions, and apply it to conic bundles over rational surfaces, quadric surface bundles over $\mathbb P^1$, and Fano threefolds.

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.

Cubic invariants for two-dimensional Hamiltonian systems are investigated using the Jacobi geometrization procedure. This approach allows for a unified treatment of invariants at both fixed and arbitrary energy. In the geometric picture the…

We study certain equivariant deformation components of minimally elliptic surface singularities under finite group actions. Interesting examples include cyclic quotients of simple elliptic singularities and finite group quotients of cusp…

Let A be a finite abelian group. We set up an algebraic framework for studying A-equivariant complex-orientable cohomology theories in terms of a suitable kind of equivariant formal groups. We compute the equivariant cohomology of many…

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

We study rationality properties of real singular cubic threefolds.

The defect of a cubic threefold $X$ with isolated singularities is a global invariant that measures the failure of $\mathbb{Q}$-factoriality. We compute the defect for such cubics in terms of topological data about the curve of lines…

We introduce an equivariant version of Hochschild cohomology as the deformation cohomology to study equivariant deformations of associative algebras equipped with finite group actions.

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