59 citations · 126 across the 10 of their papers we have counts for
10 papers
Rokhlin's signature theorems
Sergey Finashin, Viatcheslav Kharlamov, Oleg Viro
This note is written for a book dedicated to outstanding St-Petersburg mathematicians and timed to the ICM-2022 in St-Petersburg. In accordance with the plan of ICM-organizers, we…
Choreography of divisors on algebraic curves
Oleg Viro
For a non-singular real algebraic projective curve, topological restrictions on a closed motion of a simple real divisor in its linear equivalence class are found.
Hyperfields for Tropical Geometry I. Hyperfields and dequantization
Oleg Viro
New hyperfields, that is fields in which addition is multivalued, are introduced and studied. In a separate paper these hyperfields are shown to provide a base for the tropical geo…
Complex orientations of real algebraic surfaces
Oleg Viro
We study natural additional structures on real algebraic surfaces with trivial first homology mod 2 of the complexification. If the set of real points realizes the zero of the seco…
Patchworking real algebraic varieties
Oleg Viro
Patchworking is a construction of a one-parameter family of real algebraic hypersurfaces. For sufficiently small positive values of the parameter, the hypersurfaces can be obtained…
Whitney Number of Closed Real Algebraic Affine Curve of Type I
Oleg Viro
For a closed real algebraic plane affine curve dividing its complexification and equipped with a complex orientation, the Whitney number is expressed in terms of behavior of its co…