The Volume Preserving Cremona Group in Birational Geometry

Explore a 43-minute lecture on the volume preserving Cremona group, where discover the intricacies of birational automorphisms of projective spaces that preserve standard torus-invariant volume forms with logarithmic poles. Delve into the significance of this group in birational geometry and its relationship to log Calabi-Yau pairs. Learn about groundbreaking findings that demonstrate this group is neither generated by pseudo-regularizable maps nor simple, building upon Lin and Shinder's recent work on the Cremona group. Presented in collaboration with Konstantin Loginov, gain insights into advanced mathematical concepts at the intersection of algebraic geometry and group theory.