聯絡我們 網站地圖 中央大學
 
 
   
     
 
主  題
The holomorphic analytic torsion associated to some singular metrics  
 
 
 
時  間
2014-01-09 下午 2:30~4:00  
 
 
 
地  點
鴻經館 107 室  
 
 
 
主 講 者
Mounir Hajli (台北理論中心(NCTS/TPE))  
 
 
 
內  容
I will give a brief overview of the Arakelov geometry as developed by Gillet, Soulé and Bismut ([3]) and I will recall some elements of the classical spectral theory of Laplacians on compact Kähler manifold ([1]) and I will focus on the construction holomorphic analytic torsion ([2]).
The main goal of this talk is the extension of the classical spectral theory of Laplacians to a large class of singular metrics. As an application, I will consider the class of the canonical metrics on P1. These metrics are defined by the combinatorial structure of P1 viewed as a toric manifold, but unfortunately they are singular. I will introduce the notion of "canonical" holomorphic analytic torsion in this situation and give some explicit computations.

Références
[1] Nicole Berline, Ezra Getzler, and Michèle Vergne. Heat kernels and Dirac operators. Grundlehren Text Editions. Springer-Verlag, Berlin, 2004. Corrected reprint of the 1992 original.
[2] D. B. Ray and I. M. Singer. Analytic torsion for complex manifolds. Ann. of Math. (2), 98 :154–177, 1973.
[3] C. Soulé. Lectures on Arakelov geometry, volume 33 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1992. With the collaboration of D. Abramovich, J.-F. Burnol and J. Kramer.
 
   
 
附  件
 
 
 
   
 
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