Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Monodromy and Log Geometry

Seminar | October 31 | 3:45-4:45 p.m. | 939 Evans Hall

 Arthur Ogus, UC Berkeley

 Department of Mathematics

A proper semistable family over a disc gives rise to a smooth proper and saturated morphism \(X/S\) of log analytic spaces over the log disc. We will explain how the underlying map of topological spaces \(X_{top}/S_{top}\) can be recovered from the restriction \(X_0/S_0\) of \(X/S\) to the log point. We will also give simple formulas for the action of the monodromy and the differentials on the \(E_2\) terms of the “nearby cycles” spectral sequence in terms of the log structure on \(X_0/S_0\). This is joint work with Piotr Achinger.