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Star configuration points and generic plane curves


Authors: Enrico Carlini and Adam Van Tuyl
Journal: Proc. Amer. Math. Soc. 139 (2011), 4181-4192
MSC (2010): Primary 14M05, 14H50
DOI: https://doi.org/10.1090/S0002-9939-2011-11204-8
Published electronically: July 7, 2011
MathSciNet review: 2823063
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Abstract: Let $ \ell_1,\ldots,\ell_l$ be $ l$ lines in $ \mathbb{P}^2$ such that no three lines meet in a point. Let $ \mathbb{X}(l)$ be the set of points $ \{\ell_i \cap \ell_j ~\vert~ 1 \leq i < j \leq l\} \subseteq \mathbb{P}^2$. We call $ \mathbb{X}(l)$ a star configuration. We describe all pairs $ (d,l)$ such that the generic degree $ d$ curve in $ \mathbb{P}^2$ contains an $ \mathbb{X}(l)$. Our proof strategy uses both a theoretical and an explicit algorithmic approach. We also describe how one may extend our algorithmic approach to similar problems.


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Additional Information

Enrico Carlini
Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
Email: enrico.carlini@polito.it

Adam Van Tuyl
Affiliation: Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, Canada, P7B 5E1
Email: avantuyl@lakeheadu.ca

DOI: https://doi.org/10.1090/S0002-9939-2011-11204-8
Keywords: Star configurations, generic plane curves
Received by editor(s): October 13, 2010
Published electronically: July 7, 2011
Communicated by: Irena Peeva
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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