Fano mirror periods from the Frobenius structure conjecture
read the original abstract
The Fano classification program proposed by Coates-Corti-Galkin-Golyshev-Kasprzyk is based on the mirror symmetry prediction that the regularized quantum period of a Fano should be equivalent to the classical period of its mirror Landau-Ginzburg potential. We prove that this mirror equivalence follows from versions of the Frobenius structure conjecture of Gross-Hacking-Keel. We also find that the regularized quantum period, which is defined in terms of descendant Gromov-Witten numbers, is in fact given by certain naive curve counts.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
On Arithmetic Mirror Symmetry for smooth Fano fourfolds
An explicit class of tempered Laurent polynomials is defined that contains LG models for Fano threefolds and checked Fano fourfolds, enabling two new examples of Arithmetic Mirror Symmetry correspondences via Kerr's p...
-
Refined curve counting with descendants and quantum mirrors
A formula for structure constants of Bousseau's quantization of the mirror algebra for log Calabi-Yau surfaces (Y,D) in terms of higher genus descendant log GW invariants, generalizing the weak Frobenius structure con...
-
On Arithmetic Mirror Symmetry for smooth Fano fourfolds
An explicit class of tempered Laurent polynomials is introduced that includes Landau-Ginzburg models for smooth Fano threefolds and various Fano fourfolds, enabling two new examples of arithmetic mirror symmetry corre...
-
Exponential concentration for quantum periods via mirror symmetry
Modified hypergeometric series respect the exponential concentration property, implying the same for quantum periods of Fano manifolds admitting convenient weak Landau-Ginzburg models with non-negative coefficients.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.