On C-fibrations over projective curves

The goal of this paper is to present a modified version (GML) of ML invariant which should take into account rulings over a projective base and allow further stratification of smooth affine rational surfaces. We provide a non-trivial example where GML invariant is computed for a smooth affine rational surface admitting no C-actions. We apply GML invariant to computation of ML invariant of some threefolds.Comment: 21 pages, LaTe

The Freiheitssatz for Novikov algebras

We prove the Freiheitssatz for Novikov algebras in characteristic zero. It is also proved that the variety of Novikov algebras is generated by a Novikov algebra on the space of polynomials $k[x]$ in a single variable $x$ over a field $k$ with respect to the multiplication $f\circ g=\partial(f)g$. It follows that the base rank of the variety of Novikov algebras equals 1.Comment: 9 page