BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Balazs Szendroi (University of Oxford)
DTSTART:20200414T162000Z
DTEND:20200414T165000Z
DTSTAMP:20260423T005728Z
UID:NASO/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NASO/3/">The
  punctual Hilbert scheme of 4 points in affine 3-space</a>\nby Balazs Szen
 droi (University of Oxford) as part of Max Planck Institute nonlinear alge
 bra seminar online\n\n\nAbstract\nThe $n$-th punctual Hilbert scheme $\\op
 eratorname{Hilb}^n_0(\\mathbb{A}^d)$ of points of affine $d$-space paramet
 rises ideals of finite co-length $n$ of the ring of functions on $d$-dimen
 sional affine space\, whose radical is the maximal ideal at the origin (eq
 uivalently\, subschemes of length $n$ with support at the origin). A class
 ical theorem of Briancon claims the irreducibility of this space for $d=2$
  and arbitrary $n$. The case of a small number of points being straightfor
 ward\, the first nontrivial case is the case of $4$ points in $3$-space. W
 e show\, answering a question of Sturmfels\, that over the complex numbers
  $\\operatorname{Hilb}^4_0(\\mathbb{A}^3)$ is irreducible. We use a combin
 ation of arguments from computer algebra and representation theory.\n
LOCATION:https://researchseminars.org/talk/NASO/3/
END:VEVENT
END:VCALENDAR