## 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.## References

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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