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On Hurwitz-Severi numbers
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 22019 (English)In: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, ISSN 0391-173X, E-ISSN 2036-2145, Vol. 19, no 1, p. 155-167Article in journal (Refereed) Published
Abstract [en]

For a point p is an element of CP2 and a triple (g, d, l) of non-negative integers we define a Hurwitz-Severi number (hg ,d,l) as the number of generic irreducible plane curves of genus g and degree d + l having an l-fold node at p and at most ordinary nodes as singularities at the other points, such that the projection of the curve from p has a prescribed set of local and remote tangents and lines passing through nodes. In the cases d + l >= g + 2 and d + 2l >= g +2 >= d + l we express the above Hurwitz-Severi numbers via appropriate ordinary Hurwitz numbers. The remaining case d + 2l < g + 2 is still widely open.

Place, publisher, year, edition, pages
2019. Vol. 19, no 1, p. 155-167
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-167695ISI: 000459854200006OAI: oai:DiVA.org:su-167695DiVA, id: diva2:1304401
Available from: 2019-04-12 Created: 2019-04-12 Last updated: 2019-04-12Bibliographically approved

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