Vol. 9, No. 3, 2015

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Secant spaces and syzygies of special line bundles on curves

Marian Aprodu and Edoardo Sernesi

Vol. 9 (2015), No. 3, 585–600
Abstract

On a special line bundle L on a projective curve C we introduce a geometric condition called (Δq). When L = KC, this condition implies gon(C) q + 2. For an arbitrary special L, we show that (Δ3) implies that L has the well-known property (M3), generalising a similar result proved by Voisin in the case L = KC.

Keywords
projective curves, Brill–Noether theory, syzygies, secant loci
Mathematical Subject Classification 2010
Primary: 14N05
Secondary: 14N25, 14M12
Milestones
Received: 25 April 2014
Revised: 27 January 2015
Accepted: 2 March 2015
Published: 17 April 2015
Authors
Marian Aprodu
Simion Stoilow Institute of Mathematics of the Romanian Academy
P.O. Box 1-764
014700 Bucharest
Romania Faculty of Mathematics and Computer Science
University of Bucharest
14 Academiei Street
010014 Bucharest
Romania
Edoardo Sernesi
Dipartimento di Matematica e Fisica
Università degli Studi Roma Tre
Largo San Leonardo Murialdo
I-00146 Roma
Italy