Constructing the relative Fukaya category

We give a definition of Seidel's `relative Fukaya category', for a smooth complex projective variety, under a semipositivity assumption. We use the Cieliebak--Mohnke approach to transversality via stabilizing divisors. Two features of our construction are noteworthy: that we work relative to a normal crossings divisor that supports an effective ample divisor but need not have ample components; and that our relative Fukaya category is linear over a certain ring of multivariate power series with integer coefficients.

在半正定性假设下，我们给出了对于一个光滑复射影簇的塞德尔（Seidel）“相对福卡亚（Fukaya）范畴”的定义。我们使用齐列巴克 - 莫恩克（Cieliebak - Mohnke）通过稳定除子来处理横截性的方法。我们构造的两个特点值得注意：我们是相对于一个支撑有效丰富除子但各分支不一定丰富的正常交叉除子进行研究的；并且我们的相对福卡亚范畴是在某个具有整数系数的多元幂级数环上线性的。