Kyoto Journal of Mathematics

Nef cone of flag bundles over a curve

Indranil Biswas and A. J. Parameswaran

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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.

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

First available in Project Euclid: 2 June 2014

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Zentralblatt MATH identifier

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]


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.

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