Related papers: Normal generation of very ample line bundles on to…
This paper has been withdrawn.
This paper has been withdrawn by the authors because it has been combined with "Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories" (arXiv:0903.0761) together. Please see the new version of the latter paper for the…
This paper has been withdrawn by the author due to the presented idea is wrong.
This paper has been withdrawn
We reduce the problem of the projective normality of polarized abelian varieties to check the rank of very explicit matrices. This allow us to prove some results on normal generation of primitive line bundles on abelian threefolds and…
Let $X$ be a smooth projective variety over an algebraically closed field $\mathbb{K}$ with arbitrary characteristic. Suppose $L$ is an ample and globally generated line bundle. By Castelnuovo--Mumford regularity, we show that $K_X \otimes…
This paper was withdrawn by the author.
We prove results concerning the specialisation of torsion line bundles on a variety $V$ defined over $\mathbb{Q}$ to ideal classes of number fields. This gives a new general technique for constructing and counting number fields with large…
This paper has been withdrawn by the authors due to an unlikely results.
This paper has been withdrawn by the author due to extremely unscientific errors.
This paper has been withdrawn due to a copyright restrictions.
Chiriv\`{\i} and Maffei \cite{CM II} have proved that the multiplication of sections of any two ample spherical line bundles on the wonderful symmetric variety $X=\bar{G/H}$ is surjective. We have proved two criterions that allows ourselves…
This paper has been withdrawn by the author due to a error in attachment of source file.
This paper has been withdrawn by the authors due to the fact that the webs considered in the paper are ``Veronese-like webs'' which are different from Veronese webs.
This paper has been withdrawn.
Toric varieties associated with root systems appeared very naturally in the theory of group compactifications. Here they are considered in a very different context. We prove the vanishing of higher cohomology groups for certain line bundles…
This paper has been withdrawn by the author due to a new work in [arXiv:0901.0456v4] which can contain the results in this paper.
This paper has been withdrawn by the author due to an error in the proof of Theorem 2.
In this paper we construct infinitely many examples of toric Fano varieties with Picard number three, which do not admit full exceptional collections of line bundles. In particular, this disproves King's conjecture for toric Fano varieties.…
The paper is withdrawn because the analysis appeared to be incomplete.