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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On a notion of speciality of linear systems in $\mathbb {P}^n$
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by M. C. Brambilla, O. Dumitrescu and E. Postinghel PDF
Trans. Amer. Math. Soc. 367 (2015), 5447-5473 Request permission

Abstract:

Given a linear system in $\mathbb {P}^n$ with assigned multiple general points, we compute the cohomology groups of its strict transforms via the blow-up of its linear base locus. This leads us to give a new definition of expected dimension of a linear system, which takes into account the contribution of the linear base locus, and thus to introduce the notion of linear speciality. We investigate such a notion, giving sufficient conditions for a linear system to be linearly non-special for an arbitrary number of points and necessary conditions for a small number of points.
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Additional Information
  • M. C. Brambilla
  • Affiliation: Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, via Brecce Bianche, I-60131 Ancona, Italy
  • Email: brambilla@dipmat.univpm.it
  • O. Dumitrescu
  • Affiliation: Department of Mathematics, MSB 2107, University of California, Davis, California 95616
  • MR Author ID: 889839
  • Email: dolivia@math.ucdavis.edu, dumitrescu@math.uni-hannover.de
  • E. Postinghel
  • Affiliation: Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland
  • Email: epostinghel@impan.pl, elisa.postinghel@wis.kuleuven.be
  • Received by editor(s): October 24, 2012
  • Received by editor(s) in revised form: June 1, 2013
  • Published electronically: November 6, 2014
  • Additional Notes: The first author was partially supported by Italian MIUR funds
    The second author is a member of “Simion Stoilow” Institute of Mathematics of the Romanian Academy (http://www.imar.ro/)
    The third author was partially supported by Marie-Curie IT Network SAGA, [FP7/2007-2013] grant agreement PITN-GA-2008-214584
    All authors were partially supported by Institut Mittag-Leffler.
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 5447-5473
  • MSC (2010): Primary 14C20; Secondary 14J70, 14C17
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06212-0
  • MathSciNet review: 3347179