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SUMMARY:Matvey A. Sergeev
DTSTART:20260729T073000Z
DTEND:20260729T090000Z
DTSTAMP:20260728T110103Z
UID:Mos-Bei-top-seminar/152
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Mos-Bei-top-
 seminar/152/">Toric Topology of the complex Grassmann manifolds G(n\,2)</a
 >\nby Matvey A. Sergeev as part of Moscow-Beijing topology seminar\n\n\nAb
 stract\nIn toric topology and toric geometry\, a model example is the comp
 lex projective space $\\mathbb{CP}^n$ equipped with the standard actions o
 f $T^{n+1} = (U(1))^{n+1}$ and $(\\mathbb{C}^*)^{n+1}$\, respectively. In 
 this case\, the complexity of the actions is zero\, and hence the orbit sp
 ace $\\mathbb{CP}^n/T^{n+1}$ is homeomorphic to the moment polytope — th
 e simplex $\\Delta^n$. Recently\, V. M. Buchstaber and S. Terzi\\'c introd
 uced a new theory for torus actions of positive complexity. A model exampl
 e for these actions is the manifold of lines in $\\mathbb{CP}^{n-1}$\, i.e
 .\, the complex Grassmann manifold $G(n\,2)$ equipped with the standard $T
 ^n$ action. The moment polytope — the hypersimplex $\\Delta(n\,2)$ — i
 s not sufficient to describe the orbit space $G(n\,2)/T^n$. Buchstaber and
  Terzić constructed a topological model for this orbit space. A key ingre
 dient is the universal space of parameters $\\mathcal{F}$\, which is a smo
 oth compact manifold\, and a projection $\\pi \\colon \\Delta(n\,2)\\times
  \\mathcal{F} \\to G(n\,2)/T^n$. The universal space of parameters is isom
 orphic to the Chow quotient $G(n\,2)//(\\mathbb{C}^*)^n$\, introduced by I
 . M. Gelfand\, M. M. Kapranov\, and A. V. Zelevinsky. In this talk\, we wi
 ll discuss the construction of the Buchstaber–Terzi\\'c model.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/152/
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