Sergey Gorchinskiy
Isomonodromic differential equations and differential Tannakian categories.
Втр, 02/07/2012 - 15:01 — SomNambulAuthors: Alexey Ovchinnikov, Sergey Gorchinskiy
Subjects: Commutative Algebra
AbstractWe study isomonodromicity of systems of parameterized linear differential
equations and related conjugacy properties of linear differential algebraic
groups by means of differential Tannakian categories. We prove that
isomonodromicity is equivalent to isomonodromicity with respect to each
parameter separately. Also, we show that isomonodromicity is equivalent to
conjugacy to constants of the associated parameterized differential Galois
group, extending a result of P. Cassidy and M. Singer, which we also prove
categorically.- Читать далее
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Transcendence degree of zero-cycles and the structure of Chow motives.
Чт, 09/09/2010 - 15:01 — SomNambulAuthors: Sergey Gorchinskiy, Vladimir Guletskii
Subjects: Algebraic Geometry
AbstractWe show how the notion of the transcendence degree of a zero-cycle on a
smooth projective variety X is related to the structure of the motive M(X).
This can be of particular interest in the context of Bloch's conjecture,
especially for Godeaux surfaces, when the surface is given as a finite quotient
of a suitable quintic in P^3.Non-trivial elements in the Abel-Jacobi kernels of higher dimensional varieties.
Чт, 09/09/2010 - 15:01 — SomNambulAuthors: Sergey Gorchinskiy, Vladimir Guletskii
Subjects: Algebraic Geometry
AbstractWe construct non-trivial classes in the kernels of the Abel-Jacobi maps from
the Chow groups of codimension p>1 algebraic cycles to the p-th intermediate
Jacobians on higher dimensional algebraic varieties over an algebraically
closed field of characteristic zero.
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