Seidel's quintic divisor-complement conjecture
Seidel's quintic divisor-complement conjecture
Let be the quintic three-fold, let be the smooth hyperplane section used in the paper, and set . Write and for the degree-zero groups in the paper's adapted grading. Let be the canonical generator of representing the Morse–Bott family of period-one closed Reeb orbits given by the fibres of . Seidel's quintic conjecture. The small quantum product
encoding counts of rational curves and their multiple covers agrees with the family of deformed pair-of-pants products
when . The conjecture proposes a precise relationship between quantum cohomology of the quintic and symplectic cohomology of its divisor complement, potentially providing an alternative route to mirror symmetry for the quintic. It is stated without a resolution in the paper.
Sources & referencesView supporting material
Primary source
Oliver Fabert, “Higher algebraic structures in Hamiltonian Floer theory”, arXiv:1412.2682 (2019).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.