BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Dhruv Goel (Harvard University)
DTSTART:20240312T200000Z
DTEND:20240312T210000Z
DTSTAMP:20260406T162135Z
UID:agstanford/140
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/agstanford/1
 40/">Chow Classes of Varieties of Secant and Tangent Lines</a>\nby Dhruv G
 oel (Harvard University) as part of Stanford algebraic geometry seminar\n\
 nLecture held in 384-H.\n\nAbstract\n(special Student Algebraic Geometry S
 eminar\; note unusual time and location)\n\nGiven a nondegenerate smooth v
 ariety $X\\subset\\mathbb{P}^n$\, let $\\mathcal{S}(X)$ (resp. $\\mathcal{
 T}(X)$) be the subvariety of the Grassmannian $\\mathbb{G}(1\, n)=\\mathrm
 {Gr}(2\, n+1)$ of lines in $\\mathbb{P}^n$ consisting of secant (resp. tan
 gent) lines to X. I will give closed-form formulae for the classes of $\\m
 athcal{S}(X)$ and $\\mathcal{T}(X)$ in the Chow ring of $\\mathbb{G}(1\, n
 )$ in terms of the “higher degrees” of the embedding\, by a simple app
 lication of the Excess Intersection Formula on a flag variety. Using these
  formulae\, one can recover classical results about the degree of the subv
 ariety $\\mathrm{Sec}(X)$ (resp. $\\mathrm{Tan}(X)$) of $\\mathbb{P}^n$ sw
 ept out by the lines in $\\mathcal{S}(X)$ (resp. $\\mathcal{T}(X)$)\, when
  it has the expected dimension. Finally\, I will suggest potential extensi
 ons of these techniques to varieties of trisecant or bitangent lines.\n
LOCATION:https://researchseminars.org/talk/agstanford/140/
END:VEVENT
END:VCALENDAR