Kyoto Journal of Mathematics

Nef cone of flag bundles over a curve

Indranil Biswas and A. J. Parameswaran

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Abstract

Let X be a smooth projective curve defined over an algebraically closed field k, and let E be a vector bundle on X. Let OGrr(E)(1) be the tautological line bundle over the Grassmann bundle Grr(E) parameterizing all the r-dimensional quotients of the fibers of E. We give necessary and sufficient conditions for OGrr(E)(1) to be ample and nef, respectively. As an application, we compute the nef cone of Grr(E). This yields a description of the nef cone of any flag bundle over X associated to E.

Article information

Source
Kyoto J. Math., Volume 54, Number 2 (2014), 353-366.

Dates
First available in Project Euclid: 2 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1401741282

Digital Object Identifier
doi:10.1215/21562261-2642422

Mathematical Reviews number (MathSciNet)
MR3215571

Zentralblatt MATH identifier
1302.14025

Subjects
Primary: 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05] 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]

Citation

Biswas, Indranil; Parameswaran, A. J. Nef cone of flag bundles over a curve. Kyoto J. Math. 54 (2014), no. 2, 353--366. doi:10.1215/21562261-2642422. https://projecteuclid.org/euclid.kjm/1401741282


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