Algebraic Geometry Biweekly Webinar
Hironaka's Question F and its Simplification
Hironaka's Question F and its Simplification
Razieh Ahmadian, Shahid Beheshti University
1 MAY 2024
17:30 - 19:00
A special case of Hironaka's QUESTION F, named F', asks about the strong factorization of birational maps between reduced nonsingular algebraic schemes, which is still open. Suppose that $varphi : Xdashrightarrow Y$ is such a map, and let $Usubset X$ be the open subset where $varphi$ is an isomorphism. This problem asks if there exists a diagram $$xymatrix{ & Z ar[dl]_{varphi_{1}}ar[dr]^{varphi_{2}}X ar[rr]^{varphi} & & Y}$$ where the morphisms $varphi_{1}$ and $varphi_{2}$ are sequences of blow-ups of non-singular centers disjoint from $U$. In this talk, we will discuss how strong factorization can be simplified by providing a complete answer to the problem of toroidalization of morphisms, while we introduce the strong Oda conjecture.
https://zoom.us/join
Meeting ID: 9086116889
Passcode: 362880
Venue: , (Online)