Psi-floor diagrams and a Caporaso-Harris type recursion

DOI10.1007/s11856-011-0216-0zbMath1257.14041arXiv1003.2067OpenAlexW2015623694MaRDI QIDQ1760385

Florian Block, Andreas Gathmann, Hannah Markwig

Publication date: 13 November 2012

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.2067

zbMATH Keywords

Tropical geometryCaporaso--Harris type formulaFloor diagramsGromov--Witten invariants

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35)

Related Items

Polynomiality properties of tropical refined invariants, Counting tropical rational space curves with cross-ratio constraints, Refined broccoli invariants, Refined descendant invariants of toric surfaces, Tropical descendant invariants with line constraints, Counting tropical rational curves with cross-ratio constraints, Relative node polynomials for plane curves, Counting curves on Hirzebruch surfaces: tropical geometry and the Fock space, On the invariance of Welschinger invariants, Genus 0 characteristic numbers of the tropical projective plane

Cites Work

• Labeled floor diagrams for plane curves
• Mirror symmetry for \(\mathbb P^2\) and tropical geometry
• Relations between the correlators of the topological sigma-model coupled to gravity
• Counting plane curves of any genus
• Absolute and relative Gromov-Witten invariants of very ample hypersurfaces
• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• Enumeration of curves via floor diagrams
• The Caporaso-Harris formula and plane relative Gromov-Witten invariants in tropical geometry
• Tropical descendant Gromov-Witten invariants
• Computing node polynomials for plane curves
• Kontsevich's formula and the WDVV equations in tropical geometry
• Recursive Formulas for Welschinger Invariants of the Projective Plane
• Tropical fans and the moduli spaces of tropical curves
• Moduli spaces of rational tropical curves
• Floor decompositions of tropical curves : the planar case
• Notes on stable maps and quantum cohomology
• Enumerative tropical algebraic geometry in ℝ²
• Unnamed Item
• Unnamed Item