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13 papers · 2 filters
On nodal Enriques surfaces and quartic double solids
Colin Ingalls, Alexander Kuznetsov
We consider the class of singular double coverings $X \to \PP^3$ ramified in the degeneration locus of a family of 2-dimensional quadrics. These are precisely the quartic doubl…
Shells of twisted flag varieties and the Rost invariant
Skip Garibaldi, Victor Petrov, Nikita Semenov
We introduce two new general methods to compute the Chow motives of twisted flag varieties and settle a 20-year-old conjecture of Markus Rost about the Rost invariant for groups of…
Scheme of lines on a family of 2-dimensional quadrics: geometry and derived category
Alexander Kuznetsov
Given a generic family of 2-dimensional quadrics over a smooth 3-dimensional base we consider the relative Fano scheme of lines of it. The scheme has a structure of…
On the algebraic cobordism spectra MSL and MSp
Ivan Panin, Charles Walter
We construct algebraic cobordism spectra MSL and MSp. They are commutative monoids in the category of symmetric T^{2}- spectra. The spectrum MSp comes with a natural symplectic ori…
On the motivic commutative ring spectrum BO
Ivan Panin, Charles Walter
We construct an algebraic commutative ring T- spectrum BO which is stably fibrant and (8,4)- periodic and such that on SmOp/S the cohomology theory (X,U) -> BO^{p,q}(X_{+}/U_{+}) a…
Quaternionic Grassmannians and Borel classes in algebraic geometry
Ivan Panin, Charles Walter
The quaternionic Grassmannian HGr(r,n) is the affine open subscheme of the ordinary Grassmannian parametrizing those 2r-dimensional subspaces of a 2n-dimensional symplectic vector…