2022/03/16 by Tianjun Li, Tian-Jun Li, Jie Min +4 · 1 citation
Mathematics · #53D05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Calabi–Yau manifold #Cone (formal languages) #Conjecture #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematics #Pure mathematics #Symplectic Geometry (math.SG) #Symplectic geometry #Symplectomorphism #Toric variety #math.AG #math.SG #msc:53D05
paper · pdf · doi:10.48550/arxiv.2203.08544
68 pages, 26 figures. All comments are welcome!
arxiv created 2022/03/16 · openalex publication_date 2022/03/16 · arxiv updated 2022/03/17 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In this paper we are interested in the isotopy classes of symplectic log Calabi-Yau divisors in a fixed symplectic rational surface. We give several equivalent definitions and prove the stability, finiteness and rigidity results. Motivated by the problem of counting toric actions, we obtain a general counting formula of symplectic log Calabi-Yau divisors in a restrictive region of c1-nef cone. A detailed count in the case of 2- and 3-point blow-ups of complex projective space for all symplectic forms is also given. In our framework the complexity of the combinatorics of analyzing Delzant polygons is reduced to the arrangement of homology classes. Then we study its relation with almost toric fibrations. We raise the problem of realizing all symplectic log Calabi-Yau divisors by some almost toric fibrations and verify it together with another conjecture of Symington in a special region.