Gromov-Witten invariants of Fano threefolds of genera 6 and 8

2004/10/31 by Victor Przyjalkowski
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #math-ph #math.AG #math.MP #msc:14J45 #msc:14N35

paper · pdf · doi:10.1070/sm2007v198n03abeh003843

published as Math. Sb, 2007, 198 (3), 433-446. · 12 pages, 1 figure, typos corrected

arxiv created 2007/01/07 · openalex publication_date 2007/04/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to prove Golyshev's conjecture in the cases of Fano threefolds V₁₀ and V₁₄. This conjecture states modularity of D3 equations for smooth Fano threefolds with Picard group Z. More precisely, we find counting matrices of prime two-pointed Gromov-Witten invariants for them. For this we use the method that lets us find Gromov-Witten invariants of complete intersections in varieties whose invariants are (partially) known.

Citations

• On the quantum product of Schubert classes
• Stable maps and branch divisors
• Absolute and relative Gromov-Witten invariants of very ample hypersurfaces
• New recursions for genus-zero Gromov-Witten invariants