2010/10/10 by Popa, Alexandra, Aleksey Zinger, Zinger, Aleksey
Mathematics · #14N35 #53D45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1010.1946
openalex publication_date 2010/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first part of this paper, we obtain mirror formulas for twisted genus\n0 two-point Gromov-Witten (GW) invariants of projective spaces and for the\ngenus 0 two-point GW-invariants of Fano and Calabi-Yau complete intersections.\nThis extends previous results for projective hypersurfaces, following the same\napproach, but we also completely describe the structure coefficients in both\ncases and obtain relations between these coefficients that are vital to the\napplications to mirror symmetry in the rest of this paper. In the second and\nthird parts of this paper, we confirm Walcher's mirror symmetry conjectures for\nthe annulus and Klein bottle GW-invariants of Calabi-Yau complete intersection\nthreefolds; these applications are the main results of this paper. In a\nseparate paper, the genus~0 two-point formulas are used to obtain mirror\nformulas for the genus~1 GW-invariants of all Calabi-Yau complete\nintersections.\n