Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The resurgence of ideals of points and the containment problem


Authors: Cristiano Bocci and Brian Harbourne
Journal: Proc. Amer. Math. Soc. 138 (2010), 1175-1190
MSC (2010): Primary 14C20, 13C05; Secondary 14N05, 14H20, 41A05
Published electronically: December 9, 2009
MathSciNet review: 2578512
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We relate properties of linear systems on $ X$ to the question of when $ I^r$ contains $ I^{(m)}$ in the case that $ I$ is the homogeneous ideal of a finite set of distinct points $ p_1,\ldots,p_n\in\mathbf{P}^2$, where $ X$ is the surface obtained by blowing up the points. We obtain complete answers for when $ I^r$ contains $ I^{(m)}$ when the points $ p_i$ lie on a smooth conic or when the points are general and $ n\le 9$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14C20, 13C05, 14N05, 14H20, 41A05

Retrieve articles in all journals with MSC (2010): 14C20, 13C05, 14N05, 14H20, 41A05


Additional Information

Cristiano Bocci
Affiliation: Dipartimento di Scienze Matematiche e Informatiche “R. Magari”, Università degli Studi di Siena, Pian dei mantellini, 44, 53100 Siena, Italy
Email: bocci24@unisi.it

Brian Harbourne
Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588-0130
Email: bharbour@math.unl.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10108-9
PII: S 0002-9939(09)10108-9
Keywords: Fat points, symbolic powers, normal generation, projective space
Received by editor(s): March 14, 2008
Received by editor(s) in revised form: May 26, 2009
Published electronically: December 9, 2009
Additional Notes: This research was partially supported by GNSAGA of INdAM (Italy) and by the NSA
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.