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Convex Bodies Associated to Linear Series
In his work on log-concavity of multiplicities, Okounkov showed in passing that one could associate a convex body to a linear series on a projective variety, and then use convex geometry to studyExpand
Brill-Noether-Petri without degenerations
The purpose of this note is to show that curves generating the Picard group of a K3 surface X with Pic( X) = Z behave generically from the point of view of Brill-Noether theory. In particular, oneExpand
On a theorem of Castelnuovo, and the equations defining space curves
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 w Notat ion and Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 wExpand
Uniform bounds and symbolic powers on smooth varieties
The purpose of this note is to show how one can use multiplier ideals toestablish effective uniform bounds on the multiplicative behavior of certainfamilies of ideal sheaves on a smooth algebraicExpand
Singularities of theta divisors and the birational geometry of irregular varieties
The purpose of this paper is to show how the generic vanishing theorems of M. Green and the second author can be used to settle several questions and conjectures concerning the geometry of irregularExpand
Some results on the syzygies of finite sets and algebraic curves
© Foundation Compositio Mathematica, 1988, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditionsExpand
On the connectedness of degeneracy loci and special divisors
Introduction Let C be a smooth complex projective curve of genus g, and let J be the Jacobian of C. Upon choosing a base-point in C, J may be identified with the set of linear equivalence classes ofExpand
Asymptotic syzygies of algebraic varieties
We study the asymptotic behavior of the syzygies of a smooth projective variety as the positivity of the embedding line bundle grows. The main result asserts that the syzygy modules are non-zero inExpand
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