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A note on k-very ampleness of line bundles on general blow-ups of hyperelliptic surfaces  [PDF]
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.
Poincare Series And Very Ampleness Criterion For Pluri-canonical Bundles  [PDF]
Jujie Wu,Xu Wang
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.
Rank-3 stable bundles on rational ruled surfaces  [PDF]
Wei-ping Li,Zhenbo Qin
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.
Numerical Criteria for vey Ampleness of Divisors on Projective Bundles over an elliptic curve  [PDF]
Alberto Alzati,Marina Bertolini,Gian Mario Besana
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.
Effective very ampleness for generalized theta divisors  [PDF]
Eduardo Esteves,Mihnea Popa
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.
Criteria for σ-ampleness  [PDF]
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.
On k-jet ampleness of line bundles on hyperelliptic surfaces  [PDF]
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.
A note on k-jet ampleness on surfaces  [PDF]
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.
A very ampleness result
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.
A very ampleness result  [PDF]
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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