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 Lucja Farnik Mathematics , 2015, Abstract: We study k-very ampleness of line bundles on blow-ups of hyperelliptic surfaces at r very general points. We obtain a numerical condition on the number of points for which a line bundle on the blow-up of a hyperelliptic surface at these r points gives an embedding of order k.
 Mathematics , 2015, Abstract: Let $X$ be a compact quotient of a bounded domain in $\mathbb C^n$. Let $K_X$ be the canonical line bundle of $X$. In this paper, we shall introduce the notion of $S$ very ampleness for the pluri-canonical line bundles $mK_X$ by using the Poincar\'e series. The main result is an effective Seshadri constant criterion of $S$ very ampleness for $mK_X$. An elementary proof of surjectivity of the Poincar\'e map is also given.
 Mathematics , 1996, Abstract: In this paper, we compare the moduli spaces of rank-3 vector bundles stable with respect to different ample divisors over rational ruled surfaces. We also discuss the irreducibility, unirationality, and rationality of these moduli spaces.
 Mathematics , 1997, Abstract: In Butler, J.Differential Geom. 39 (1):1--34,1994, the author gives a sufficient condition for a line bundle associated with a divisor D to be normally generated on $X=P(E)$ where E is a vector bundle over a smooth curve C. A line bundle which is ample and normally generated is automatically very ample. Therefore the condition found in Butler's work, together with Miyaoka's well known ampleness criterion, give a sufficient condition for the very ampleness of D on X. This work is devoted to the study of numerical criteria for very ampleness of divisors D which do not satisfy the above criterion, in the case of C elliptic. Numerical conditions for the very ampleness of D are proved,improving existing results. In some cases a complete numerical characterization is found.
 Mathematics , 2003, Abstract: Given a smooth projective curve X, we give effective very ampleness bounds for generalized theta divisors on the moduli spaces $SU_X(r,d)$ and $U_X(r,d)$ of semistable vector bundles of rank r and degree d on X with fixed, respectively arbitrary, determinant.
 Dennis S. Keeler Mathematics , 1999, DOI: 10.1090/S0894-0347-00-00334-9 Abstract: In the noncommutative geometry of Artin, Van den Bergh, and others, the twisted homogeneous coordinate ring is one of the basic constructions. Such a ring is defined by a $\sigma$-ample divisor, where $\sigma$ is an automorphism of a projective scheme X. Many open questions regarding $\sigma$-ample divisors have remained. We derive a relatively simple necessary and sufficient condition for a divisor on X to be $\sigma$-ample. As a consequence, we show right and left $\sigma$-ampleness are equivalent and any associated noncommutative homogeneous coordinate ring must be noetherian and have finite, integral GK-dimension. We also characterize which automorphisms $\sigma$ yield a $\sigma$-ample divisor.
 Lucja Farnik Mathematics , 2015, Abstract: We study k-jet ampleness of line bundles on hyperelliptic surfaces using vanishing theorems. Our main result states that on a hyperelliptic surface of an arbitrary type a line bundle of type (m,m) with m\geq k+2 is k-jet ample.
 Adrian Langer Mathematics , 1998, Abstract: We prove Reider type criterions for k-jet spannedness and k-jet ampleness of adjoint bundles for surfaces with at most rational singularities. Moreover, we prove that on smooth surfaces [n(n+4)/4]-very ampleness implies n-jet ampleness.
 Antonio Laface Le Matematiche , 1997, Abstract: Let (M, L) be a polarized manifold. The aim of this paper is to establish a connection between the generators of the graded algebra oplus_{i≥1} H^0(M, i L) and the very ampleness of the line bundle r L . Some applications are given.
 Antonio Laface Mathematics , 2001, Abstract: Let (M,L) be a polarized manifold and let G(M,L) be the graded algebra generated by H^0(M,iL) in degree i. The aim of this paper is to establish a connection between the generators of G(M,L) and the very ampleness of the line bundle rL. Some applications are given.
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