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SUMMARY:Douglas Guimarães (UNICAMP)
DTSTART:20201028T183000Z
DTEND:20201028T200000Z
DTSTAMP:20260423T021708Z
UID:BRAG/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BRAG/28/">Mo
 duli spaces of quasitrivial rank 2 sheaves</a>\nby Douglas Guimarães (UNI
 CAMP) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nDougl
 as Guimarães (UNICAMP)\n\nTitle: Moduli spaces of quasitrivial rank 2 she
 aves\n\nAbstract: A torsion free sheaf $E$ on $\\mathbb{P}^3$ is called qu
 asitrivial if $E^{\\vee\\vee}=\\mathcal{O}_{\\mathbb{P}^3}^{\\oplus r}$ an
 d $\\dim(E^{\\vee\\vee}/E)=0$. While such sheaves are always $\\mu$-semis
 table\, they may not be Gieseker semistable. We study the moduli spaces of
  $\\mu$- and Gieseker semistable quasitrivial sheaves of rank 2 via the q
 uot scheme of points $Quot(\\mathcal{O}_{\\mathbb{P}^3}^{\\oplus 2}\,n)$\,
  where $n=h^0(E^{\\vee\\vee}/E)$. We will show the construction of an irre
 ducible component of the Gieseker moduli space which is birrational to the
  total space of a $\\mathbb{P}^{n-1}$-bundle over $S(n-1)\\times\\mathbb{P
 }^3$\, where $S(n)$ is the smoothable component of the Hilbert scheme of $
 n$ points in $ \\mathbb{P}^3$. Furthermore\, this is the only irreducible 
 component when $n\\le10$.\n
LOCATION:https://researchseminars.org/talk/BRAG/28/
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