Center for Complex Geometry

Algebraic Geometry Day at CCG in IBS
2021-12-09 | B266, IBS, Korea, Republic of
List of Seminars

On the Singular Loci of Higher Secants of Veronese Varieties
Kangjin Han (DGIST)
14:00-14:50, online

Manin’s Conjecture for a Log Del Pezzo Surface of Index 2
DongSeon Hwang (Ajou Univ.)
15:20-16:10, IBS B266

Ulrich Bundles on Cubic Fourfolds
Yeongrak Kim (Pusan National Univ.)
16:30-17:20, IBS B266

Kangjin Han, On the Singular Loci of Higher Secants of Veronese Varieties
2021-12-09 14:00 - 14:50 (Asia/Seoul) | on-line
Speaker

Kangjin Han
DGIST

(This is a part of Algebraic Geometry Day at CCG in IBS.)
For a projective variety X in PN, the k-secant variety σk(X) is defined to be the closure of the union of k-planes in PN spanned by k-points of X. In this talk, we consider singular loci of higher secant varieties of the image of the d-uple Veronese embedding of projective n-space, νd(Pn). For the singular loci of k-secant of νd(Pn), it has been known only for k≤3. First, I will review some basic notions and results and then explain projective techniques with respect to an explicit calculation of the Gauss map of X and computation for conormal space via a certain type of Young flattening. As investigating geometry of moving tangents along subvarieties, we determine the (non-)singularity of so-called ‘subsecant loci’ of k-secant of νd(Pn) for arbitrary k. This is a joint work with Katsuhisa Furukawa.
