Birational Geometry of Sextic Double Solids with a Compound A_n Singularity

Explore the birational geometry of sextic double solids with compound A_n singularities in this 53-minute lecture by Erik Paemurru from the University of Miami/IMSA. Delve into the properties of these lowest degree Gorenstein Fano 3-folds, examining their expected rigid behavior in terms of birational geometry. Learn about the known birational rigidity of smooth sextic double solids and those with ordinary double points. Discover the speaker's findings on the limitations of n in compound A_n singularities and the failure of rigidity for n greater than 3. Cover topics such as material variety, parameterization theorem, divisorial contraction, weighted blowups, Kawakita's Theorem, and the construction of divisor contractions.

Introduction
Material Variety
Compound AnSingularities
Parameterization
Theorem
Divisorial contraction
Definitions
Weighted Blowups
Kawakitas Theorem
Weight respecting maps
Construction of divisor contractions