Simplicial arrangements and the geometry of planar cubic curves

YMSC Topology Seminar

Organizers：

陈伟彦、高鸿灏、黄意、林剑锋

Speaker：

Guillaume TAHAR

BIMSA

Time：

Thur., 16:00-17:00, Oct. 17, 2024

Venue：

B725, Shuangqing Complex Building

清华大学双清综合楼A座B725

Online：

Zoom Meeting ID: 405 416 0815

Passcode: 111111

Title：

Simplicial arrangements and the geometry of planar cubic curves

Abstract:

In their solution to the orchard-planting problem, Green and Tao established a structure theorem which proves that in a line arrangement in the real projective plane with few double points, most lines are tangent to the dual curve of a cubic curve. We provide geometric arguments to prove that in the case of a simplicial arrangement, the aforementioned cubic curve cannot be irreducible. It follows that Grünbaum's conjectural asymptotic classification of simplicial arrangements holds under the additional hypothesis of a linear bound on the number of double points. This is a joint work with Dmitri Panov.