Oct 09, 2012
Tuesday

03:45 PM  06:00 PM


Commutative Algebra and Algebraic Geometry (Eisenbud Seminar)
Giulio Caviglia, Bernd Sturmfels (UC Berkeley Math Faculty)

 Location
 UC Berkeley
 Video


 Abstract
 October 9
3:45: Bernd Sturmfels
A Hilbert Scheme in Computer Vision
Multiview geometry is the study of twodimensional images of threedimensional scenes, a foundational subject in computer vision. We determine a universal Groebner basis for the multiview ideal of n generic cameras. As the cameras move, the multiview varieties vary in a family of dimension 11n15. This family is the distinguished component of a multigraded Hilbert scheme with a unique Borelfixed point. We present a combinatorial study of ideals lying on that Hilbert scheme. This is joint work with Chris Aholt and Rekha Thomas.
5pm: Giulio Caviglia
Koszul property of projections of the Veronese cubic surface
Let V be the Veronese cubic surface in P^9. We classify the projections of V to P^8 whose coordinate rings are Koszul. In particular we obtain a purely theoretical proof of the Koszulness of the pinched Veronese, a result obtained originally by using filtrations, deformations and computer assisted computations. To this purpose we extend, to certain complete intersections, results of Conca, Herzog, Trung and Valla concerning homological properties of diagonal algebras. This is a joint work with Aldo Conca.
 Supplements



