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SUMMARY:Isabelle Charton (Instituto Superior Técnico\, Universidade de Li
 sboa)
DTSTART:20260630T140000Z
DTEND:20260630T150000Z
DTSTAMP:20261023T085130Z
UID:Geolis/181
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/181/"
 >Monotone Symplectic Manifolds with a Torus Action of Complexity One</a>\n
 by Isabelle Charton (Instituto Superior Técnico\, Universidade de Lisboa)
  as part of Geometria em Lisboa (IST)\n\n\nAbstract\nA compact symplectic 
 manifold $(M\, \\omega)$ is called positive monotone if its first Chern cl
 ass is a positive multiple of $[\\omega]$ in the second de Rham group $H^2
 (M)$. A smooth Fano variety is a complex manifold\, whose anti-canonical l
 ine bundle is ample. Such a variety can be endowed with a symplectic form 
 such that it becomes a positive monotone symplectic manifold. For this rea
 son\, positive monotone symplectic manifolds are considered the symplectic
  counterparts of smooth Fano varieties.\n\nIn the field of symplectic geom
 etry\, a general outstanding issue is understanding in what context positi
 ve monotone symplectic manifolds differ from Fano varieties. In low dimens
 ions\, namely two and four\, it has been proven by Gromov\, Taubes\, McDuf
 f\, and Ohat-Ono that any positive monotone symplectic manifold is symplec
 tomorphic to a Fano variety. Starting from dimension twelve\, work by Fine
  and Panov provides examples of positive monotone symplectic manifolds tha
 t are not even homotopy equivalent to a Fano variety.\n\nIn this talk\, I 
 will explain what is known about the differences between Fano varieties an
 d positive monotone symplectic manifolds endowed with a Hamiltonian action
  of a compact torus $T$. In particular\, I will present new results for th
 e case where the complexity of the action is one\, i.e.\, $\\frac{1}{2}\\d
 im(M)-\\dim(T)=1$.\n\nThis talk is based on joint work with Liat Kessler\,
  Silvia Sabatini\, and Daniele Sepe.\n
LOCATION:https://researchseminars.org/talk/Geolis/181/
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