The resurgence of ideals of points and the containment problem
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- by Cristiano Bocci and Brian Harbourne PDF
- Proc. Amer. Math. Soc. 138 (2010), 1175-1190 Request permission
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
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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
- MR Author ID: 217048
- Email: bharbour@math.unl.edu
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1175-1190
- MSC (2010): Primary 14C20, 13C05; Secondary 14N05, 14H20, 41A05
- DOI: https://doi.org/10.1090/S0002-9939-09-10108-9
- MathSciNet review: 2578512