Related papers: Birational types of algebraic orbifolds

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 arithmetic properties of equivariant birational types introduced by Kontsevich, Pestun, and the second author.

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

We construct a birational invariant for certain algebraic group actions. We use this invariant to classify linear representations of finite abelian groups up to birational equivalence, thus answering, in a special case, a question of E. B.…

A priori, the set of birational transformations of an algebraic variety is just a group. We survey the possible algebraic structures that we may add to it, using in particular parametrised family of birational transformations.

A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally…

This paper introduces a novel framework for constructing invariants in $G$-equivariant birational geometry by unifying two recent approaches: the theory of atoms recently developed by Katzarkov, Kontsevich, Pantev, and Yu, and the theory of…

In this paper we study birational Kleinian groups, i.e.\ groups of birational transformations of complex projective varieties acting in a free, properly discontinuous and cocompact way on an open set of the variety with respect to the usual…

We study relations between the classical modular symbols associated with congruence subgroups and Kontsevich-Pestun-Tschinkel groups $\mathcal{M}_n(G)$ associated with finite abelian groups $G$.

In this paper, we discuss the birational invariance of the class of balanced hyperbolic manifolds.

We survey new results on finite groups of birational transformations of algebraic varieties.

The simultaneous invariants of 2, 3, 4 and 5 ternary quadratic forms under the group $\SL(3, {\Bbb C})$ were given by several authors (P. Gordan, C. Ciamberlini, H.W. Turnbull, J.A Todd), utilizing the symbolic method. Using the Jordan…

We show that when two toric Calabi-Yau 3-folds and their corresponding toric varieties are related by a birational transformation, they are associated with a pair of dimer models on the 2-torus that define dimer integrable systems, which…

We investigate the birational geometry of Deligne-Mumford stacks and define new birational invariants in this context.

In this paper we present a general framework for Berezin covariant symbols, and we discuss a few basic properties of the corresponding symbol map, with emphasis on its injectivity in connection with some problems in representation theory of…

We discuss invariants in equivariant birational geometry.

We study the structure of combinatorial Burnside groups, which receive equivariant birational invariants of actions of finite groups on algebraic varieties.

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.