Crossing the Transcendental Divide: From Translation Surfaces to Algebraic Curves
DC Element | Wert | Sprache |
---|---|---|
dc.contributor.author | Celik, Tuerkue Oezluem | |
dc.contributor.author | Fairchild, Samantha | |
dc.contributor.author | Mandelshtam, Yelena | |
dc.date.accessioned | 2023-07-12T06:56:49Z | - |
dc.date.available | 2023-07-12T06:56:49Z | - |
dc.date.issued | 2023 | |
dc.identifier.issn | 1058-6458 | |
dc.identifier.uri | http://osnascholar.ub.uni-osnabrueck.de/handle/unios/71956 | - |
dc.description.abstract | We study constructing an algebraic curve from a Riemann surface given via a translation surface, which is a collection of finitely many polygons in the plane with sides identified by translation. We use the theory of discrete Riemann surfaces to give an algorithm for approximating the Jacobian variety of a translation surface whose polygon can be decomposed into squares. We first implement the algorithm in the case of L shaped polygons where the algebraic curve is already known. The algorithm is also implemented in any genus for specific examples of Jenkins-Strebel representatives, a dense family of translation surfaces that, until now, lived squarely on the analytic side of the transcendental divide between Riemann surfaces and algebraic curves. Using Riemann theta functions, we give numerical experiments and resulting conjectures up to genus 5. | |
dc.language.iso | en | |
dc.publisher | TAYLOR & FRANCIS INC | |
dc.relation.ispartof | EXPERIMENTAL MATHEMATICS | |
dc.subject | algebraic curves | |
dc.subject | DISCRETE RIEMANN SURFACES | |
dc.subject | JACOBIAN NULLWERTE | |
dc.subject | Mathematics | |
dc.subject | Riemann surfaces | |
dc.subject | Riemann theta functions | |
dc.subject | THETA | |
dc.subject | Translation surfaces | |
dc.title | Crossing the Transcendental Divide: From Translation Surfaces to Algebraic Curves | |
dc.type | journal article | |
dc.identifier.doi | 10.1080/10586458.2023.2203413 | |
dc.identifier.isi | ISI:000993310600001 | |
dc.identifier.eissn | 1944-950X | |
dc.publisher.place | 530 WALNUT STREET, STE 850, PHILADELPHIA, PA 19106 USA | |
dcterms.isPartOf.abbreviation | Exp. Math. | |
dcterms.oaStatus | Green Submitted | |
local.import.remains | affiliations : Bogazici University; University Osnabruck; University of California System; University of California Berkeley | |
local.import.remains | earlyaccessdate : MAY 2023 | |
local.import.remains | web-of-science-index : Science Citation Index Expanded (SCI-EXPANDED) |
Seitenaufrufe
2
Letzte Woche
2
2
Letzter Monat
2
2
geprüft am 08.06.2024