Categorically Absorbing Singularities

Aporva Varshney (UCL)

Tuesday 25th March 15:00-16:00 Maths 311B

Abstract

Even if we want to work with smooth varieties, we may eventually have to contend with the thorny reality of singularities. We will explore how we can deal with singularities at the level of the derived category by looking at results from Kuznetsov-Shinder for nodal varieties, where one can sometimes produce a semiorthogonal decomposition of the derived category into a ‘smooth’ component and a ‘singular’ component. Crucially, this ‘singular’ component behaves well under smoothings, allowing us to relate the derived categories of two smooth varieties by degenerating and then resolving. We will also give an overview of results for other singularities in the literature, including work looking at a non-isolated singularity (arXiv:2402.18513).

Add to your calendar

Download event information as iCalendar file (only this event)