A remark on very ample linear series

We give a criterium on the existence of (e - 1)-very ample linear series on a general k-gonal curve of genus $g (e \geq 1)$, and we add some general remarks on such series.     

A remark on very ample linear series: II

The distribution of complete and very ample linear series on a curve X of genus g is only well known if they satisfy the inequality g−d + r ≤ 1, for their index of speciality. In this paper we mainly study those curves X on which all complete and very ample satisfy this inequality. The interesting case g = 9 is discussed in detail.     

A remark on Weierstrass points and linear series on multiple covering curves

Here we study multiple coverings of rational and irational curves. We give a theorem about the non-gap sequence on m-gonal curves. We then study general irrational covering f ： X→ C, and say when h^0（X, f^＊（L）） = h^0（C,L） for L line bundle on C.     

A remark on linear permutation polynomials

We give an explicit representation of the class of linear permutation polynomials. By the representation, the number of them can be computed easily.     

Notes on very ample vector bundles on 3-folds

Let be a very ample vector bundle of rank two on a smooth complex projective threefold X. An inequality about the third Segre class of is provided when is nef but not big, and when a suitable positive multiple of defines a morphism X → B with connected fibers onto a smooth projective curve B, where K_X is the canonical bundle of X. As an application, the case where the genus of B is positive and has a global section whose zero locus is a smooth hyperelliptic curve of genus ≧ 2 is investigated, and our previous result is improved for threefolds. Received: 27 January 2005; revised: 26 March 2005     

Very ample linear systems on abelian varieties

The first author is partially supported by N.S.F. grant DMS 92-03919 and the European Science Project Geometry of Algebraic Varieties, contract no. SCI-0398-C (A)     

Effective bounds for very ample line bundles

Let be an ample line bundle on a non singular projective -fold . It is first shown that is very ample for . The proof develops an original idea of Y.T. Siu and is based on a combination of the Riemann-Roch theorem together with an improved Noetherian induction technique for the Nadel multiplier ideal sheaves. In the second part, an effective version of the big Matsusaka theorem is obtained, refining an earlier version of Y.T. Siu: there is an explicit polynomial bound of degree in the arguments, such that is very ample for . The refinement is obtained through a new sharp upper bound for the dualizing sheaves of algebraic varieties embedded in projective space. Oblatum 30-I-1995 & 18-V-1995     

Parabolic ample bundles III: Numerically effective vector bundles

In this continuation of [Bi2] and [BN], we define numerically effective vector bundles in the parabolic category. Some properties of the usual numerically effective vector bundles are shown to be valid in the more general context of numerically effective parabolic vector bundles.     

A remark on equational classes generated by very small free algebras

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