Vector bundles on proper toric 3-folds and certain other schemes
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- by Markus Perling and Stefan Schröer PDF
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Abstract:
We show that a proper algebraic $n$-dimensional scheme $Y$ admits non-trivial vector bundles of rank $n$, even if $Y$ is non-projective, provided that there is a modification containing a projective Cartier divisor that intersects the exceptional locus in only finitely many points. Moreover, there are such vector bundles with arbitrarily large top Chern number. Applying this to toric varieties, we infer that every proper toric threefold admits such vector bundles of rank three. Furthermore, we describe a class of higher-dimensional toric varieties for which the result applies, in terms of convexity properties around rays.References
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Additional Information
- Markus Perling
- Affiliation: Fakultät für Mathematik, Universität Bielefeld, Postfach 100 131, 33501 Bielefeld, Germany
- MR Author ID: 727662
- Email: perling@math.uni-bielefeld.de
- Stefan Schröer
- Affiliation: Mathematisches Institut, Heinrich-Heine-Universität, 40204 Düsseldorf, Germany
- MR Author ID: 630946
- Email: schroeer@math.uni-duesseldorf.de
- Received by editor(s): November 4, 2014
- Received by editor(s) in revised form: July 16, 2015
- Published electronically: November 28, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 4787-4815
- MSC (2010): Primary 14J60, 14M25
- DOI: https://doi.org/10.1090/tran/6813
- MathSciNet review: 3632550