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SUMMARY:Alessio Caminata (University of Genoa\, Genoa\, Italy)
DTSTART:20230127T120000Z
DTEND:20230127T130000Z
DTSTAMP:20260423T021046Z
UID:VCAS/159
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/159/">D
 eterminantal varieties from point configurations on hypersurfaces</a>\nby 
 Alessio Caminata (University of Genoa\, Genoa\, Italy) as part of IIT Bomb
 ay Virtual Commutative Algebra Seminar\n\n\nAbstract\nPoint configurations
  appear naturally in different contexts\, ranging from the study of the ge
 ometry of data sets to questions in commutative algebra and algebraic geom
 etry concerning determinantal varieties and invariant theory. In this talk
 \, we bring these perspectives together: we consider the scheme X_{r\,d\,n
 } parametrizing n ordered points in r-dimensional projective space that li
 e on a common hypersurface of degree d. We show that this scheme has a det
 erminantal structure and\, if r>1\, we prove that it is irreducible\, Cohe
 n-Macaulay\, and normal. Moreover\, we give an algebraic and geometric des
 cription of the singular locus of X_{r\,d\,n} in terms of Castelnuovo-Mumf
 ord regularity and d-normality. This yields a complete characterization of
  the singular locus of X_{2\,d\,n} and X_{3\,2\,n}. This is joint work wit
 h Han-Bom Moon and Luca Schaffler.\n
LOCATION:https://researchseminars.org/talk/VCAS/159/
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