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On a Conjecture of Butler

In: Analytic and Algebraic Geometry

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  • Usha N. Bhosle

    (Indian Institute of Science, Department of Mathematics)

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].

Suggested Citation

  • Usha N. Bhosle, 2017. "On a Conjecture of Butler," Springer Books, in: Anilatmaja Aryasomayajula & Indranil Biswas & Archana S. Morye & A. J. Parameswaran (ed.), Analytic and Algebraic Geometry, pages 29-48, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-5648-2_3
    DOI: 10.1007/978-981-10-5648-2_3
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