Birational superrigidity and K-stability

Algebraic and Tropical Geometry
Event time: 
Thursday, October 11, 2018 - 3:00pm
HLH17 03
17 Hillhouse Ave, Basement level, room 3
New Haven, CT 06511
Ziquan Zhuang
Speaker affiliation: 
Princeton University
Event description: 

Birational superrigidity and K-stability are properties of Fano varieties that have many interesting geometric implications. For instance, birational superrigidity implies non-rationality and K-stability is related to the existence of Kähler-Einstein metrics. Nonetheless, both properties are hard to verify in general. In this talk, I will first explain how to relate birational superrigidity to K-stability using alpha invariants; I will then outline a method of proving birational superrigidity that works quite well with most families of index one Fano complete intersections and thereby also verify their K-stability. This is partly based on joint work with Charlie Stibitz and Yuchen Liu.