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Vanishing theorems for linearly obstructed divisors

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journal contribution
posted on 01.02.2017 by Olivia Dumitrescu, Elisa Postinghel
We study divisors on the blow-up of Pn at points in general position that are non-special with respect to the notion of linear speciality introduced in [6]. We describe the cohomology groups of their strict transforms via the blow-up of the space along their linear base locus. We extend the result to non-effective divisors that sit in a small region outside the effective cone. As an application, we describe linear systems of divisors in Pn blown-up at points in star configuration and their strict transforms via the blow-up of the linear base locus.

Funding

The authors thank the organisors of the Workshop on Perspectives and Emerging Topics in Algebra and Combinatorics -PEAKs 2013 (Austria), funded by DFG Conference Grant HA4383/6-1 for the hospitality during their stay that promoted and made this collaboration possible.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Algebra

Volume

477

Pages

312-359

Citation

POSTINGHEL, E. and DUMITRESCU, O., 2017. Vanishing theorems for linearly obstructed divisors. Journal of Algebra, 477 (May), pp.312-359.

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

10/01/2017

Publication date

2017-01-16

Notes

This paper was published in the journal Journal of Algebra and the definitive published version is available at http://dx.doi.org/10.1016/j.jalgebra.2017.01.006.

ISSN

0021-8693

Language

en

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