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SUMMARY:Katsuhisa Furukawa (Josai University)
DTSTART:20210330T100000Z
DTEND:20210330T110000Z
DTSTAMP:20260423T053014Z
UID:ZAG/107
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ZAG/107/">On
  the singular loci of higher secant varieties of Veronese embeddings</a>\n
 by Katsuhisa Furukawa (Josai University) as part of ZAG (Zoom Algebraic Ge
 ometry) seminar\n\n\nAbstract\nFor a projective variety X in P^N\, the k-s
 ecant variety \\sigma_k(X) is defined to be the closure of the union of k-
 planes in P^N spanned by k-points of X. It is well known that \\sigma_{k-1
 }(X) is contained in the singular locus of \\sigma_k(X). Let us consider t
 he case when X is the image of the Veronese embedding P^n to P^N of degree
  d\, where N = \\binom{d+N}{d}-1. In the case of k=3\, K. Han showed that 
 \\Sing(\\sigma_3(X)) = \\sigma_2(X)\, except when d=4 and n > 2. In the ex
 ceptional case\, \\Sing(\\sigma_3(X)) is the union of \\sigma_2(X) and D\,
  where D is an irreducible subset. In this talk\, we first give a geometri
 c description of this D for k = 3\, and next study the case of k > 3. In p
 articular\, I will explain projective techniques with respect to an explic
 it calculation of the Gauss map of X and the projection from the incidence
  correspondence of \\sigma_k(X). This is a joint work with Kangjin Han.\n
LOCATION:https://researchseminars.org/talk/ZAG/107/
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