UNSPECIFIED (2003) Linear systems of plane curves with a composite number of base points of equal multiplicity. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 355 (2). pp. 539-549. ISSN 0002-9947

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Abstract

In this article we study linear systems of plane curves of degree d passing through general base points with the same multiplicity at each of them. These systems are known as homogeneous linear systems. We especially investigate for which of these systems, the base points, with their multiplicities, impose independent conditions and which homogeneous systems are empty. Such systems are called non-special. We extend the range of homogeneous linear systems that are known to be non-special. A theorem of Evain states that the systems of curves of degree d with 4(h) base points with equal multiplicity are non-special. The analogous result for 9(h) points was conjectured. Both of these will follow, as corollaries, from the main theorem proved in this paper. Also, the case of 4(h)9(k) points will follow from our result. The proof uses a degeneration technique developed by C. Ciliberto and R. Miranda.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Publisher:	AMER MATHEMATICAL SOC
ISSN:	0002-9947
Date:	2003
Volume:	355
Number:	2
Number of Pages:	11
Page Range:	pp. 539-549
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/10455

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