arXiv subjects
Publications and source records attributed to Ren Fernandes.
To establish a basis of the sheaf theoretical study of the Milnor fibers and monodromies of complete intersection varieties, we clarify the structures of the Verdier specialization sheaves associated to them. Assuming the Thom condition in a direction, some basic results on them will be obtained. Then we apply them to obtain formulas for the Euler obstructions of complete intersection varieties having non-isolated singular points.
For a smooth morphism $f: X \longrightarrow \Sigma$ of real analytic manifolds and an $\mathbb{R}$-constructible sheaf $F$ on $X$ satisfying some condition, we define a family of Lagrangian cycles parameterized by $\Sigma$ that we call the relative characteristic cycle of $F$ for $f$. In this way, the theory of characteristic cycles due to Kashiwara and Schapira is naturally extended to the relative setting. Based on it, we then prove a formula for the characteristic cycles of real nearby cycle sheaves. This leads us to obtain also formulas for the characteristic cycles of various constructible sheaves, such as specialization, microlocalization, and complex nearby and vanishing cycle sheaves, in a unified manner. In fact, our methods allow us to calculate not only their characteristic cycles but also their microlocal types in many situations. We will illustrate it by various examples.