Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Linear systems in $ \mathbb{P}^2$ with base points of bounded multiplicity


Author: Stephanie Yang
Journal: J. Algebraic Geom. 16 (2007), 19-38
DOI: https://doi.org/10.1090/S1056-3911-06-00447-4
Published electronically: September 21, 2006
MathSciNet review: 2257318
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Abstract | References | Additional Information

Abstract: We present a proof of the Harbourne-Hirschowitz conjecture for linear systems with multiple points of order $ 7$ or less. This uses a well-known degeneration of the plane developed by Ciliberto and Miranda as well as a combinatorial game that arises from specializing points onto lines.


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Additional Information

Stephanie Yang
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: styang@umich.edu

DOI: https://doi.org/10.1090/S1056-3911-06-00447-4
Received by editor(s): January 30, 2005
Received by editor(s) in revised form: September 5, 2005, and November 1, 2005
Published electronically: September 21, 2006

American Mathematical Society