## Linear systems of plane curves with base points of equal multiplicity

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- by Ciro Ciliberto and Rick Miranda PDF
- Trans. Amer. Math. Soc.
**352**(2000), 4037-4050 Request permission

## Abstract:

In this article we address the problem of computing the dimension of the space of plane curves of degree $d$ with $n$ general points of multiplicity $m$. A conjecture of Harbourne and Hirschowitz implies that when $d \geq 3m$, the dimension is equal to the expected dimension given by the Riemann-Roch Theorem. Also, systems for which the dimension is larger than expected should have a fixed part containing a multiple $(-1)$-curve. We reformulate this conjecture by explicitly listing those systems which have unexpected dimension. Then we use a degeneration technique developed to show that the conjecture holds for all $m \leq 12$.## References

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## Additional Information

**Ciro Ciliberto**- Affiliation: Dipartimento of Mathematics, Universitá di Roma II, Via Fontanile di Carcaricola, 00173 Rome, Italy
- MR Author ID: 49480
- Email: cilibert@axp.mat.utovrm.it
**Rick Miranda**- Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
- Email: miranda@math.colostate.edu
- Received by editor(s): July 1, 1998
- Published electronically: April 21, 2000
- Additional Notes: Research supported in part by the NSA
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**352**(2000), 4037-4050 - MSC (1991): Primary 14H50, 14J26
- DOI: https://doi.org/10.1090/S0002-9947-00-02416-8
- MathSciNet review: 1637062