The Hasse problem for rational surfaces.
The Hodge Conjecture for Fourfolds Admitting a Covering by Rational Curves.
The jacobian map, the jacobian group and the group of automorphisms of the Grassmann algebra
There are nontrivial dualities and parallels between polynomial algebras and the Grassmann algebras (e.g., the Grassmann algebras are dual of polynomial algebras as quadratic algebras). This paper is an attempt to look at the Grassmann algebras at the angle of the Jacobian conjecture for polynomial algebras (which is the question/conjecture about the Jacobian set– the set of all algebra endomorphisms of a polynomial algebra with the Jacobian – the Jacobian conjecture claims that the Jacobian...
The Modell-Weil groups of unirational quasi-elliptic surfaces in characteristic 3.
The non rationality of the generic Enriques' threefold
The rationality of some moduli spaces of plane curves
Torsion in K2 of fields and 0-cycles on rational surfaces.
Transformation Groups on Homogeneous-Rational Manifolds.
Twistor spaces with a pencil of fundamental divisors.