Equivariant Burnside groups and toric varieties
We study $G$-equivariant birational geometry of toric varieties, where $G$ is a finite group.
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arXiv subjects
Yuri Tschinkel
Publications and source records attributed to Yuri Tschinkel.
Equivariant Burnside groups and representation theory
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.
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Equivariant Burnside groups: structure and operations
We introduce and study functorial and combinatorial constructions concerning equivariant Burnside groups.
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Rationality of even-dimensional intersections of two real quadrics
We study rationality constructions for smooth complete intersections of two quadrics over nonclosed fields. Over the real numbers, we establish a criterion for rationality in dimension four.
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Arithmetic properties of equivariant birational types
We study arithmetic properties of equivariant birational types introduced by Kontsevich, Pestun, and the second author.
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Symbols and equivariant birational geometry in small dimensions
We discuss the equivariant Burnside group and related new invariants in equivariant birational geometry, with a special emphasis on applications in low dimensions.
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Equivariant birational types and Burnside volume
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 properties. We establish a specialization map for the equivariant birational type of a smooth algebraic variety with an action of a finite group.
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Birational types of algebraic orbifolds
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.
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Rationality of Fano threefolds of degree 18 over nonclosed fields
We study unirationality and rationality of Fano threefolds of degree 18 over nonclosed fields.
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Equivariant birational geometry and modular symbols
We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups.
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Cycle class maps and birational invariants
We introduce new obstructions to rationality for geometrically rational threefolds arising from the geometry of curves and their cycle maps.
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Cubic fourfolds fibered in sextic del Pezzo surfaces
We exhibit new examples of rational cubic fourfolds, parametrized by a countably infinite union of codimension-two subvarieties in the moduli space. Our examples are fibered in sextic del Pezzo surfaces over the projective plane; they are rational whenever the fibration has a rational section.
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Fibrations in sextic del Pezzo surfaces with mild singularities
We study sextic del Pezzo surface fibrations via root stacks.
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Rationality of complete intersections of two quadrics
We study rationality problems for smooth complete intersections of two quadrics. We focus on the three-dimensional case, with a view toward understanding the invariants governing the rationality of a geometrically rational threefold over a non-closed field.
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Varieties of planes on intersections of three quadrics
We study the geometry of spaces of planes on smooth complete intersections of three quadrics, with a view toward rationality questions.
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Brauer groups of involution surface bundles
We present an algorithm to compute the Brauer group of involution surface bundles over rational surfaces.
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Potentially stably rational del Pezzo surfaces over nonclosed fields
We classify Galois actions on Picard lattices of del Pezzo surfaces of degrees 1,2, and 3 giving rise to minimal surfaces with no cohomological obstructions to stable rationality.
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Involution surface bundles over surfaces
We construct models of involution surface bundles over algebraic surfaces, degenerating over normal crossing divisors, and with controlled singularities of the total space.
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