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SUMMARY:Ritvik Ramkumar (Berkeley)
DTSTART:20210806T190000Z
DTEND:20210806T200000Z
DTSTAMP:20260407T215020Z
UID:agstanford/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/agstanford/5
 6/">On the tangent space to the Hilbert scheme of points in $\\mathbf{P}^3
 $</a>\nby Ritvik Ramkumar (Berkeley) as part of Stanford algebraic geometr
 y seminar\n\n\nAbstract\nThe Hilbert scheme of $n$ points in $\\mathbf{P}^
 2$ is smooth of dimension $2n$ and the tangent space to any monomial subsc
 heme admits a pleasant combinatorial description. On the other hand\, the 
 Hilbert scheme of $n$ points in $\\mathbf{P}^3$ is almost always singular 
 and there is a conjecture by Briançon and Iarrobino describing the monomi
 al subscheme with the largest tangent space dimension. In this talk we wil
 l generalize the combinatorial description to the Hilbert scheme of points
  in $\\mathbf{P}^3$\, revealing new symmetries in the tangent space to any
  monomial subscheme. We will use these symmetries to prove many cases of t
 he conjecture and strengthen previous bounds on the dimension of the Hilbe
 rt scheme. In addition\, we will also characterize smooth monomial points 
 on the Hilbert scheme. This is joint work with Alessio Sammartano.\n
LOCATION:https://researchseminars.org/talk/agstanford/56/
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