Constructing the relative Fukaya category. (English) Zbl 07871029
The main result of the paper under review is a construction of the relative Fukaya category of a smooth complex projective variety relative to a simple normal crossings divisor, under a semipositivity assumption. See P. Seidel’s lectures on the subject [Fukaya categories and Picard-Lefschetz theory. Zürich: European Mathematical Society (EMS) (2008; Zbl 1159.53001)].
This is a special case of a more general, purely symplectic construction. Two features of the construction are noteworthy according to the authors: that they work relative to a normal crossings divisor which supports an effective ample divisor but need not have ample components; and that their relative Fukaya category is linear over a certain ring of multivariate power series with integer coefficients.
This is a special case of a more general, purely symplectic construction. Two features of the construction are noteworthy according to the authors: that they work relative to a normal crossings divisor which supports an effective ample divisor but need not have ample components; and that their relative Fukaya category is linear over a certain ring of multivariate power series with integer coefficients.
Reviewer: Zdzisław Dzedzej (Gdańsk)
MSC:
| 18G70 | \(A_{\infty}\)-categories, relations with homological mirror symmetry |
| 14D05 | Structure of families (Picard-Lefschetz, monodromy, etc.) |
| 53D37 | Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category |
