2017/06/16 by Renzo Cavalieri, Paul Johnson, Cavalieri, Renzo +5 · 2 citations
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1706.05401
openalex publication_date 2017/06/16 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
We study the stationary descendant Gromov-Witten theory of toric surfaces by\ncombining and extending a range of techniques - tropical curves, floor\ndiagrams, and Fock spaces. A correspondence theorem is established between\ntropical curves and descendant invariants on toric surfaces using maximal toric\ndegenerations. An intermediate degeneration is then shown to give rise to floor\ndiagrams, giving a geometric interpretation of this well-known bookkeeping tool\nin tropical geometry. In the process, we extend floor diagram techniques to\ninclude descendants in arbitrary genus. These floor diagrams are then used to\nconnect tropical curve counting to the algebra of operators on the bosonic Fock\nspace, and are shown to coincide with the Feynman diagrams of appropriate\noperators. This extends work of a number of researchers, including\nBlock-G "ottche, Cooper -Pandharipande, and Block-Gathmann-Markwig.\n