On the unboundedness of birational automorphisms

Time：Fri., 15:30-16:30, Nov. 7, 2025

Venue：B725, Shuangqing Complex Building A

Organizer：Caucher Birkar，Jia Jia

Speaker：Hsueh-Yung Lin

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，贾甲

Speaker：

Hsueh-Yung Lin 林学庸 (台湾大学)

Time：

Fri., 15:30-16:30, Nov. 7, 2025

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Venue:

B725, Shuangqing Complex Building A

Title:

On the unboundedness of birational automorphisms

Abstract:

We formulate boundedness questions for birational automorphisms and discuss to which extent the Cremona groups exhibit unbounded behavior. As an example, we show that over a field of characteristic zero, the weak factorization centers occurring in the Cremona transformations of P^N do not belong to a birationally bounded family whenever N ≥ 4, even after cancellations up to birational equivalence of their MRC bases. (Based on joint work with Evgeny Shinder.)

DATENovember 6, 2025

Related News

0
The birational geometry of matroids
AbstractIn this talk, I will consider isomorphisms of Bergman fans of matroids. Motivated by algebraic geometry, these isomorphisms can be considered as matroid analogs of birational maps. I will introduce Cremona automorphisms of the coarsest fan structure. These produce a class of automorphisms which do not come from automorphisms of the underlying matroid. I will then explain that the automo...
1
Fixed-point-free fusion automorphisms
AbstractUnderstanding the symmetries of algebraic objects can help decrease their complexity by several fold, and this reduction in complexity is intensified when there are fewer and fewer fixed-points. Typically one requires the unit or neutral element to be fixed by any symmetry, so a symmetry for which this is the only fixed-point has been called "fixed-point-free". These are the most active...