Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Amoebas of curves and the Lyashko-Looijenga map
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 12019 (English)In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. 100, no 1, p. 301-322Article in journal (Refereed) Published
Abstract [en]

For any curve V in a toric surface X, we study the critical locus S subset of V of the moment map mu from V to its compactified amoeba mu(V). For any complete linear system |L| given by an ample line bundle L on X, we show that the critical locus S subset of V is smooth as long as the curve V is outside of a subset of real codimension 1 in |L|. In particular, the complement of the latter subset appears to be disconnected for general L. It suggests a classification problem analogous to Hilbert's Sixteenth Problem, namely the topological classification of pairs (V,S) for curves V is an element of|L|. The description of the critical locus S in terms of the logarithmic Gau ss map gamma:V -> CP1 relates the latter problem to the study of the Lyashko-Looijenga map (ll). The map ll associates to a generic curve V is an element of|L| the unordered set of the critical values of gamma on CP1. We prove two statements concerning ll that are crucial for our classification problem: the map ll is algebraic; the map ll extends to nodal curves in |L|. This fact allows us to construct many examples of pairs (V,S) by perturbing nodal curves.

Place, publisher, year, edition, pages
2019. Vol. 100, no 1, p. 301-322
Keywords [en]
14H50, 14M25 (primary)
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-171669DOI: 10.1112/jlms.12214ISI: 000478598500013OAI: oai:DiVA.org:su-171669DiVA, id: diva2:1344569
Available from: 2019-08-21 Created: 2019-08-21 Last updated: 2019-08-21Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Search in DiVA

By author/editor
Lang, Lionel
By organisation
Department of Mathematics
In the same journal
Journal of the London Mathematical Society
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 10 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf