Recovery of Plane Curves from Branch Points.
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| Title: | Recovery of Plane Curves from Branch Points. |
|---|---|
| Authors: | Agostini, Daniele1 (AUTHOR), Markwig, Hannah1 (AUTHOR), Nollau, Clemens1 (AUTHOR), Schleis, Victoria1 (AUTHOR), Sendra-Arranz, Javier2 (AUTHOR), Sturmfels, Bernd2,3 (AUTHOR) bernd@mis.mpg.de |
| Source: | Discrete & Computational Geometry. Sep2024, Vol. 72 Issue 2, p451-475. 25p. |
| Subjects: | Algebraic geometry, Hurwitz polynomials, Number systems, Orbits (Astronomy), Algorithms |
| Abstract: | We recover plane curves from their branch points under projection onto a line. Our focus lies on cubics and quartics. These have 6 and 12 branch points respectively. The plane Hurwitz numbers 40 and 120 count the orbits of solutions. We determine the numbers of real solutions, and we present exact algorithms for recovery. Our approach relies on 150 years of beautiful algebraic geometry, from Clebsch to Vakil and beyond. [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 179949814 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Recovery of Plane Curves from Branch Points. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Agostini%2C+Daniele%22">Agostini, Daniele</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Markwig%2C+Hannah%22">Markwig, Hannah</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Nollau%2C+Clemens%22">Nollau, Clemens</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Schleis%2C+Victoria%22">Schleis, Victoria</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sendra-Arranz%2C+Javier%22">Sendra-Arranz, Javier</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sturmfels%2C+Bernd%22">Sturmfels, Bernd</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<i> bernd@mis.mpg.de</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+%26+Computational+Geometry%22">Discrete & Computational Geometry</searchLink>. Sep2024, Vol. 72 Issue 2, p451-475. 25p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Algebraic+geometry%22">Algebraic geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Hurwitz+polynomials%22">Hurwitz polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Number+systems%22">Number systems</searchLink><br /><searchLink fieldCode="DE" term="%22Orbits+%28Astronomy%29%22">Orbits (Astronomy)</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We recover plane curves from their branch points under projection onto a line. Our focus lies on cubics and quartics. These have 6 and 12 branch points respectively. The plane Hurwitz numbers 40 and 120 count the orbits of solutions. We determine the numbers of real solutions, and we present exact algorithms for recovery. Our approach relies on 150 years of beautiful algebraic geometry, from Clebsch to Vakil and beyond. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00454-023-00538-5 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: 451 Subjects: – SubjectFull: Algebraic geometry Type: general – SubjectFull: Hurwitz polynomials Type: general – SubjectFull: Number systems Type: general – SubjectFull: Orbits (Astronomy) Type: general – SubjectFull: Algorithms Type: general Titles: – TitleFull: Recovery of Plane Curves from Branch Points. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Agostini, Daniele – PersonEntity: Name: NameFull: Markwig, Hannah – PersonEntity: Name: NameFull: Nollau, Clemens – PersonEntity: Name: NameFull: Schleis, Victoria – PersonEntity: Name: NameFull: Sendra-Arranz, Javier – PersonEntity: Name: NameFull: Sturmfels, Bernd IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 01795376 Numbering: – Type: volume Value: 72 – Type: issue Value: 2 Titles: – TitleFull: Discrete & Computational Geometry Type: main |
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