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Cuspidal curves and Heegaard Floer homology
Renyi Inst Math, Realtanoda 13-15, H-1053 Budapest, Hungary..
Univ Florence, Dept Math & Informat, Viale Morgagni 67-A, I-50134 Florence, Italy..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
2016 (English)In: Proceedings of the London Mathematical Society, ISSN 0024-6115, E-ISSN 1460-244X, Vol. 112, no 3, 512-548 p.Article in journal (Refereed) Published
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Text
Abstract [en]

We give bounds on the gap functions of the singularities of a cuspidal plane curve of arbitrary genus, generalising recent work of Borodzik and Livingston. We apply these inequalities to unicuspidal curves whose singularity has one Puiseux pair: we prove two identities tying the parameters of the singularity, the genus and the degree of the curve; we improve on some degree-multiplicity asymptotic inequalities; finally, we prove some finiteness results, we construct infinite families of examples, and, in some cases, we give an almost complete classification.

Place, publisher, year, edition, pages
2016. Vol. 112, no 3, 512-548 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-288619DOI: 10.1112/plms/pdv074ISI: 000372606900003OAI: oai:DiVA.org:uu-288619DiVA: diva2:927094
Funder
Knut and Alice Wallenberg Foundation
Available from: 2016-05-11 Created: 2016-04-28 Last updated: 2017-02-20Bibliographically approved

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