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<p class="MsoNormal" style="background:white"><span style="color:black">Dear all,<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black">I forward the invitation to a talk at the UvA on K-stability for anyone who might be interested.<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black">Best wishes,<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black">Gabriele<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black"><a href="https://sites.google.com/view/anne-sophie-kaloghiros/home" target="_blank" title="https://sites.google.com/view/anne-sophie-kaloghiros/home">Anne-Sophie Kaloghiros</a> (Brunel
University London) <o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black">Wednesday 14<sup>th</sup> of May at 11am<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black">KdVI, seminar room F3.20 (on the third floor)<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black">Title: Explicit K-stability and moduli construction of Fano 3-folds<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black">Abstract: The Calabi problem asks which compact complex manifolds are Kähler-Einstein (KE)- i.e. can be endowed with a canonical metric that satisfies both an algebraic condition (being
Kähler) and the Einstein (partial differential) equation. Such manifolds always have a canonical class of definite sign. The existence of such a metric on manifolds with positive and trivial canonical class (general type and Calabi Yau) was proved in the 70s.
In the case of Fano manifolds the situation is more subtle - Fano manifolds may or may not have a KE metric.<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black">We now know that a Fano manifold admits a KE metric precisely when it satisfies a sophisticated algebro-geometric condition called K-polystability. Surprisingly, K-polystability also sheds
some light on another important problem: while Fano varieties do not behave well in families, K-polystable Fano varieties do and form K-moduli spaces.<o:p></o:p></span></p>
<p class="MsoNormal" style="background:white"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">Our explicit understanding of K-polystability is still partial, and few examples of K-moduli spaces are known. In dimension 3, Fano manifolds were classified into 105 deformation families by Mori-Mukai and Iskovskikh.
In this talk, I will present an overview of the Calabi problem, and discuss its solution in dimension 3. Knowing - as we do - which families in the classification of Fano 3-folds have K-polystable members is a starting point to investigate the corresponding
K-moduli spaces. I will describe explicitly some K-moduli spaces of Fano 3-folds.</span><span lang="en-NL" style="font-size:11.0pt;mso-fareast-language:EN-US"><o:p></o:p></span></p>
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