A line bundle L on a smooth curve X is nonspecial if and only if L admits a presentation L=K_X -D +E for some effective divisors D and E>0 on X with gcd (D, E)=0 and h^0 (X, O_X (D))=1. In this work, we define a minimal presentation of L which is minimal with respect to the degree of E among the presentations. If L=K_X -D +E with degE>2 is a minimal, then L is very ample and any q-points of X with q <degE are embedded in general position but the points of E are not. We investigate sufficient… Expand

We shall work over the complex number field C. Let X be a non-singular projective curve of genus g. We always assume that it is non-hyperelliptic and sometimes identify it with its canonical image in… Expand

ABSTRACT In this article, we prove that the inner projection of a projective curve with higher linear syzygies has also higher linear syzygies. Specifically, if a very ample line bundle ℒ on a smooth… Expand

For a smooth curve C it is known that a very ample line bundle $${\mathcal{L}}$$ on C is normally generated if Cliff($${\mathcal{L}}$$) < Cliff(C) and there exist extremal line bundles… Expand

This chapter discusses Brill-Noether theory on a moving curve, and some applications of that theory in elementary deformation theory and in tautological classes.Expand

Review of the deformation theory of compact complex manifolds.- Structure of Hol(V, ?1).- Rn(V) for n?g.- Families of holomorphic maps of compact complex manifolds.- Families of effective divisors… Expand