Seminario Nacional de Geometría Algebraica en línea

Resumen:

En esta charla, introduciremos las condiciones de estabilidad para variedades algebraicas. Veremos el caso particular de las condiciones sobre curvas y los problemas que involucra estudiar estabilidad desde este enfoque, así como algunas opciones para atacar dichos problemas, por ejemplo, curvas en superficies y, si el tiempo lo permite, diferenciales cuadráticas sobre la curva.

Resumen: In this talk, I discuss a joint work with Alexey Elagin and Evgeny Shinder that lies at the intersection of birational and derived geometry. What kind of geometric information is encoded in the derived category of a variety, and how does this information behave under birational maps?

Resumen: 

We consider the case of surfaces equipped with a group action, and show that their derived categories admit a canonical (mutation-equivalence class of) semi-orthogonal decomposition that "behaves well" with respect to birational geometry. We call such decompositions "atomic". If time permits, I will discuss applications to (bi-)rationality questions.

This talk is intended for non-experts; all notions will be explained.