Varieties with and dim
Varieties with small dual varieties, I.
Vector bundles of finite rank on complete intersections of finite codimension in ind-Grassmannians
In this article we establish an analogue of the Barth-Van de Ven-Tyurin-Sato theorem.We prove that a finite rank vector bundle on a complete intersection of finite codimension in a linear ind-Grassmannian is isomorphic to a direct sum of line bundles.
Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology
Here we study vector bundles E on the Hirzebruch surface F e such that their twists by a spanned, but not ample, line bundle M = Fe(h + ef) have natural cohomology, i.e. h 0(F e, E(tM)) > 0 implies h 1(F e, E(tM)) = 0.
Vector bundles on non-Kaehler elliptic principal bundles
We study relatively semi-stable vector bundles and their moduli on non-Kähler principal elliptic bundles over compact complex manifolds of arbitrary dimension. The main technical tools used are the twisted Fourier-Mukai transform and a spectral cover construction. For the important example of such principal bundles, the numerical invariants of a 3-dimensional non-Kähler elliptic principal bundle over a primary Kodaira surface are computed.
Vector Bundles over Affine Surfaces.
Versal deformation of Hopf surfaces.
Very Ample Divisors on Rational Surfaces.
Very ample line bundles on blown-up projective varieties.
Very ampleness of multiples of principal polarization on degenerate Abelian surfaces.
Quite recently, Alexeev and Nakamura proved that if Y is a stable semi-Abelic variety (SSAV) of dimension g equipped with the ample line bundle OY(1), which deforms to a principally polarized Abelian variety, then OY(n) is very ample as soon as n ≥ 2g + 1, that is n ≥ 5 in the case of surfaces. Here it is proved, via elementary methods of projective geometry, that in the case of surfaces this bound can be improved to n ≥ 3.
Von der Zerlegung der Discriminante der cubischen Gleichung, welche die Hauptaxen einer Fläche zweiter Ordnung bestimmen, in eine Summe von Quadraten.