A Mehta–Ramanathan theorem for linear systems with basepoints. Issue 10 (11th January 2016)

• Record Type: Journal Article
• Authors: Graf, Patrick
• Is Part Of: Mathematische Nachrichten. Volume 289:Issue 10(2016)
• Page Start: 1208
• Page End: 1218
• Publication Date: 2016-01-11
• Subjects: Semistable sheaves -- Mehta–Ramanathan theorem -- complete intersection curves -- generic semipositivity -- 14F05 -- 14H60 -- 14J60; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201500180
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : Let ( X, H ) be a normal complex projective polarized variety and E an H ‐semistable sheaf on X . We prove that the restriction E | C to a sufficiently positive general complete intersection curve C ⊂ X passing through a prescribed finite set of points S ⊂ X remains semistable, provided that at each p ∈ S, the variety X is smooth and the factors of a Jordan–Hölder filtration of E are locally free. As an application, we obtain a generalization of Miyaoka's generic semipositivity theorem.