A 4₃ configuration of lines and conics in ℙ⁵
Studying the connection between the title configuration and Kummer surfaces we write explicit quadratic equations for the latter. The main results are presented in Theorems 8 and 16.
A bound on the geometric genus of projective varieties
A classification of toric varieties with few generators.
A criterion for a variety to be cone.
Algebraic geometry and local differential geometry
Ample vector bundles with sections vanishing along conic fibrations over curves.
Asymptotic behaviour of numerical invariants of algebraic varieties
We show that if the degree of a nonsingular projective variety is high enough, maximization of any of the most important numerical invariants, such as class, Betti number, and any of the Chern or middle Hodge numbers, leads to the same class of extremal varieties. Moreover, asymptotically (say, for varieties whose total Betti number is big enough) the ratio of any two of these invariants tends to a well-defined constant.