- Path:
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Arithmetic counts of tropical plane curves and their properties
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Periodical
- Title:
- Advances in geometry
- Publication:
-
Berlin [u.a.]: de Gruyter
- Note:
- Gesehen am 26.06.20
- Scope:
- Online-Ressource
- ISSN:
- 1615-7168
- ZDB-ID:
-
2043066-8
- Keywords:
- Geometrie ; Zeitschrift
- Classification:
- Mathematik
- DDC Group:
- 500 Naturwissenschaften
- Collection:
- Mathematik
- Copyright:
- Rights reserved
- Accessibility:
- Eingeschränkter Zugang mit Nutzungsbeschränkungen
- Title:
- Advances in geometry
- Publication:
-
Berlin [u.a.]: de Gruyter
- Note:
- Gesehen am 26.06.20
- Scope:
- Online-Ressource
- ISSN:
- 1615-7168
- ZDB-ID:
-
2043066-8
- Keywords:
- Geometrie ; Zeitschrift
- Classification:
- Mathematik
- DDC Group:
- 500 Naturwissenschaften
- Collection:
- Mathematik
- Copyright:
- Rights reserved
- Accessibility:
- Eingeschränkter Zugang mit Nutzungsbeschränkungen
Article
- Title:
- Arithmetic counts of tropical plane curves and their properties
- Publication:
-
Berlin [u.a.]: de Gruyter, 2024
- Language:
- English
- Information:
- Abstract: Recently, the first and third author proved a correspondence theorem which recovers the Levine- Welschinger invariants of toric del Pezzo surfaces as a count of tropical curves weighted with arithmetic multiplicities. In this paper, we study properties of the arithmetic count ofplane tropical curves satisfying point conditions. We prove that this count is independent of the configuration of point conditions. Moreover, a Caporaso- Harris formula for the arithmetic count of plane tropical curves is obtained by moving one point to the very left. Repeating this process until all point conditions are stretched, we obtain an enriched count of floor diagrams which coincides with the tropical count. Finally, we prove polynomiality properties for the arithmetic counts using floor diagrams.
- Scope:
- Online-Ressource
- Note:
- Kein Open Access
- Archivierung/Langzeitarchivierung gewährleistet
- Keywords:
- Gromov-Witten invariant ; Welschinger invariant ; tropical curve ; arithmetic count ; 14N10 ; 14N35 ; 14T20 ; 14T25 ; 14P99
- Classification:
- Mathematik
- Sonstiges
- Collection:
- Mathematik
- Sonstiges
- Copyright:
- Rights reserved
- Accessibility:
- Eingeschränkter Zugang mit Nutzungsbeschränkungen
- Title:
- Arithmetic counts of tropical plane curves and their properties
- Publication:
-
Berlin [u.a.]: de Gruyter, 2024
- Language:
- English
- Information:
- Abstract: Recently, the first and third author proved a correspondence theorem which recovers the Levine- Welschinger invariants of toric del Pezzo surfaces as a count of tropical curves weighted with arithmetic multiplicities. In this paper, we study properties of the arithmetic count ofplane tropical curves satisfying point conditions. We prove that this count is independent of the configuration of point conditions. Moreover, a Caporaso- Harris formula for the arithmetic count of plane tropical curves is obtained by moving one point to the very left. Repeating this process until all point conditions are stretched, we obtain an enriched count of floor diagrams which coincides with the tropical count. Finally, we prove polynomiality properties for the arithmetic counts using floor diagrams.
- Scope:
- Online-Ressource
- Note:
- Kein Open Access
- Archivierung/Langzeitarchivierung gewährleistet
- Keywords:
- Gromov-Witten invariant ; Welschinger invariant ; tropical curve ; arithmetic count ; 14N10 ; 14N35 ; 14T20 ; 14T25 ; 14P99
- Classification:
- Mathematik
- Sonstiges
- Collection:
- Mathematik
- Sonstiges
- Copyright:
- Rights reserved
- Accessibility:
- Eingeschränkter Zugang mit Nutzungsbeschränkungen
