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Limits of PGL(3)-translates of plane curves, II
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).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, 548-564 p.Article in journal (Refereed) Published
Abstract [en]

Every complex plane curve C determines a subscheme J of the P-8 of 3 x 3 matrices, whose projective normal cone (PNC) captures subtle invariants of C. In [P. Aluffi, C. Faber, Limits of PGL(3)-translates of plane curves, I, J. Pure Appl. Algebra 214 (5) (2010) 526-547] we obtain a set-theoretic description of the PNC and thereby we determine all possible limits of families of plane curves whose general element is isomorphic to C. The main result of this article is the determination of the PNC as a cycle; this is an essential ingredient in our computation in [P. Aluffi, C. Faber, Linear orbits of arbitrary plane curves, Michigan Math. J. 48 (2000) 1-37] of the degree of the PGL(3)-orbit closure of an arbitrary plane curve, an invariant of natural enumerative significance.

Place, publisher, year, edition, pages
2010. Vol. 214, no 5, 548-564 p.
Keyword [en]
linear orbits
Identifiers
URN: urn:nbn:se:kth:diva-19249DOI: 10.1016/j.jpaa.2009.06.012ISI: 000274866900005Scopus ID: 2-s2.0-73549102638OAI: oai:DiVA.org:kth-19249DiVA: diva2:337296
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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