Arithmetic Geometry and Number Theory RTG Seminar: Dual Complex of a Singular Pair

Seminar | February 11 | 3-5 p.m. | 748 Evans Hall

 Chenyang Xu, MIT

 Department of Mathematics

The topology of an algebraic variety is a central subject in algebraic geometry. Instead of a variety, we consider the topology of a pair (X,D) which is a variety X with a divisor D, but in the coarsest level. More precisely, we study the dual complex defined as the combinatorial datum characterizing how the components of D intersect with each other. We will discuss how to use the minimal model program (MMP) to investigate it. We will also discuss some applications, including in the construction of non-archimedean SYZ fibrations.