Catalan-many tropical morphisms to trees; Part I: Constructions. (May 2021)
- Record Type:
- Journal Article
- Title:
- Catalan-many tropical morphisms to trees; Part I: Constructions. (May 2021)
- Main Title:
- Catalan-many tropical morphisms to trees; Part I: Constructions
- Authors:
- Draisma, Jan
Vargas, Alejandro - Abstract:
- Abstract: We investigate the tree gonality of a genus- g metric graph, defined as the minimum degree of a tropical morphism from any tropical modification of the metric graph to a metric tree. We give a combinatorial constructive proof that this number is at most ⌈ g / 2 ⌉ + 1, a fact whose proofs so far required an algebro-geometric detour via special divisors on curves. For even genus, the tropical morphism which realizes the bound belongs to a family of tropical morphisms that is pure of dimension 3 g − 3 and that has a generically finite-to-one map onto the moduli space of genus- g metric graphs. Our methods focus on the study of such families. This is part I in a series of two papers: in part I we fix the combinatorial type of the metric graph to show a bound on tree-gonality, while in part II we vary the combinatorial type and show that the number of tropical morphisms, counted with suitable multiplicities, is the same Catalan number that counts morphisms from a general genus- g curve to the projective line.
- Is Part Of:
- Journal of symbolic computation. Volume 104(2021)
- Journal:
- Journal of symbolic computation
- Issue:
- Volume 104(2021)
- Issue Display:
- Volume 104, Issue 2021 (2021)
- Year:
- 2021
- Volume:
- 104
- Issue:
- 2021
- Issue Sort Value:
- 2021-0104-2021-0000
- Page Start:
- 580
- Page End:
- 629
- Publication Date:
- 2021-05
- Subjects:
- Tropical geometry -- Gonality -- Metric graph -- Tropical morphism -- Balancing condition
Mathematics -- Data processing -- Periodicals
Numerical analysis -- Data processing -- Periodicals
Automatic programming (Computer science) -- Periodicals
Mathématiques -- Informatique -- Périodiques
Analyse numérique -- Informatique -- Périodiques
Programmation automatique -- Périodiques
Automatic programming (Computer science)
Mathematics -- Data processing
Numerical analysis -- Data processing
Periodicals
Electronic journals
510.285 - Journal URLs:
- http://www.sciencedirect.com/science/journal/07477171 ↗
http://www.elsevier.com/journals ↗ - DOI:
- 10.1016/j.jsc.2020.09.005 ↗
- Languages:
- English
- ISSNs:
- 0747-7171
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 5067.900000
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 22181.xml