论文标题
派生的关键基因座上的衍生的拉格朗日纤维
A Derived Lagrangian Fibration on the Derived Critical Locus
论文作者
论文摘要
我们研究拉格朗日形态的衍生相交的符号几何形状。特别是，我们表明，对于功能性$ f：x \ rightarrow \ mathbb {a} _k^1 $，派生的关键基因座具有自然的拉格朗日纤维化$ \ textbf {crit}（f）（f）\ rightarrow x $。如果$ f $是非分类且严格的关键基因座平滑的情况，我们表明派生的关键基因座上的拉格朗日纤维由黑森二次形式确定。
We study the symplectic geometry of derived intersections of Lagrangian morphisms. In particular, we show that for a functional $f : X \rightarrow \mathbb{A}_k^1$, the derived critical locus has a natural Lagrangian fibration $\textbf{Crit}(f) \rightarrow X$. In the case where $f$ is non-degenerate and the strict critical locus is smooth, we show that the Lagrangian fibration on the derived critical locus is determined by the Hessian quadratic form.
