Related papers: Arithmetic properties of equivariant birational ty…
We introduce a variant of the birational symbols group of Kontsevich, Pestun, and the second author, and use this to define birational invariants 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…
In arXiv:2404.19088, we initiated a program linking birational invariants with smooth ones and offering new interpretations of classical invariants, such as the Kervaire-Milnor invariants. Here, we rely on the profound geometric reasoning…
We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups.
In this note, we sketch an approach to the problems of equivariant birational geometry developed by M. Kontsevich and Yu. Tschinkel, where Burnside invariants were introduced. We are making explicit the role of Nori constructions in this…
We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.
We discuss invariants in equivariant birational geometry.
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.
In this paper we give an attempt to extend some arithmetic properties such as multiplicativity, convolution products to the setting of operators theory. We provide a significant examples which are of interest in number theory. We also give…
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…
In this sequel to arxiv:arXiv:1012.0835 we develop Bezout type theorems for semidegrees (including an explicit formula for {\em iterated semidegrees}) and an inequality for subdegrees. In addition we prove (in case of surfaces) a Bernstein…
This is a commentary on Raoul Bott and Loring Tu's joint article "Equivariant characteristic classes in the Cartan model," which appeared in "Geometry, Analysis, and Applications (Varanasi, 2000)," World Scientif Publishing, River Edge, NJ,…
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…
We study linear actions of finite groups in small dimensions, up to equivariant birationality.
Using the methods of classical invariant theory a general approach to finding of identities for Bernulli, Euler and Hermite polynomials is proposed.
Geometric Invariant Theory (GIT) produces quotients of algebraic varieties by reductive groups. If the variety is projective, this quotient depends on a choice of polarisation; by work of Dolgachev-Hu and Thaddeus, it is known that two…
We discuss the equivariant Burnside group and related new invariants in equivariant birational geometry, with a special emphasis on applications in low dimensions.
We consider a sequence of four variable polynomials by refining Stieltjes' continued fraction for Eulerian polynomials. Using combinatorial theory of Jacobi-type continued fractions and bijections we derive various combinatorial…
The modified Bernoulli numbers \begin{equation*} B_{n}^{*} = \sum_{r=0}^{n} \binom{n+r}{2r} \frac{B_{r}}{n+r}, \quad n > 0 \end{equation*} introduced by D. Zagier in 1998 were recently extended to the polynomial case by replacing $B_{r}$ by…
We study $G$-equivariant birational geometry of toric varieties, where $G$ is a finite group.