On a Conjecture of Butler

Usha N. Bhosle ()
Additional contact information
Usha N. Bhosle: Indian Institute of Science, Department of Mathematics

A chapter in Analytic and Algebraic Geometry, 2017, pp 29-48 from Springer

Abstract: Abstract Syzygy bundles over smooth curves (as well as higher dimensional smooth varieties) have been studied for several years now. Let L be a line bundle on a smooth curve X. Given a subspace V of the space of sections of L which generates L, the kernel M L,V of the evaluation map $$ V \otimes {\mathcal{O}}_{x} \to L $$ is called a Syzygy bundle or a Kernel bundle or a Lazarfeld bundle. These bundles have several applications, applications to Syzygy problems, Greens conjectures, Minimal Resolution conjectures, Theta functions, Picard bundles. They also play an important role in Brill-Noether theory for higher ranks and coherent systems. Eighteen years back, D.C. Butler made a conjecture about the semistability of M L,V for general (L, V ) [15]. The conjecture was proved recently by Peter Newstead, myself and Leticia Brambila-Paz [8].

Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-5648-2_3

Ordering information: This item can be ordered from
http://www.springer.com/9789811056482

DOI: 10.1007/978-981-10-5648-2_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().