Secant spaces and syzygies of special line bundles on curves

Aprodu, Marian; Sernesi, Edoardo

doi:10.2140/ant.2015.9.585

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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

DOI: 10.2140/ant.2015.9.585

Abstract

On a special line bundle $L$ on a projective curve $C$ we introduce a geometric condition called $(Δ_{q})$ . When $L = K_{C}$ , this condition implies $gon (C) \geq q + 2$ . For an arbitrary special $L$ , we show that $(Δ_{3})$ implies that $L$ has the well-known property $(M_{3})$ , generalising a similar result proved by Voisin in the case $L = K_{C}$ .

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

Vol. 9, No. 3, 2015