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Limits of PGL(3)-translates of plane curves, I
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2598-4870
2010 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 214, no 5, 526-547 p.Article in journal (Refereed) Published
Abstract [en]

We classify all possible limits of families of translates of a fixed, arbitrary complex plane curve. We do this by giving a set-theoretic description of the projective normal cone (PNC) of the base scheme of a natural rational map, determined by the curve, from the P-8 of 3 x 3 matrices to the P-N of plane curves of degree d. In a sequel to this paper we determine the multiplicities of the components of the PNC. The knowledge of the PNC as a cycle is essential in our computation of the degree of the PGL(3)-orbit closure of an arbitrary plane curve, performed in [P. Aluffi, C. Faber, Linear orbits of arbitrary plane curves, Michigan Math. J. 48(2000) 1-37].

Place, publisher, year, edition, pages
2010. Vol. 214, no 5, 526-547 p.
Keyword [en]
linear orbits
URN: urn:nbn:se:kth:diva-19248DOI: 10.1016/j.jpaa.2009.06.010ISI: 000274866900004ScopusID: 2-s2.0-73549099077OAI: diva2:337295
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2010-12-10Bibliographically approved

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