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Seminar of Algebraic Geometry in East Asia
 
15:00 - 16:00, December 18, 2020 (Friday)
broadcast in Room 515, Cosmology Bldg., NTU, Online seminar
(線上演講 於台大次震宇宙館515教室直播/收播)
Positivity in Hyperkähler Manifolds via Rozansky—Witten Theory
Chen Jiang (Fudan University)

Abstract:

For a hyperkähler manifold of dimension , Huybrechts showed that there are constants such that
 
 
for any line bundle $L$ on , where is the Beauville--Bogomolov--Fujiki quadratic form of . Here the polynomial is called the Riemann--Roch polynomial of .
 
In this talk, I will discuss recent progress on the positivity of coefficients of the Riemann--Roch polynomial and also positivity of Todd classes. Such positivity results follows from a Lefschetz-type decomposition of the root of Todd genus via the Rozansky—Witten theory, following the ideas of Hitchin, Sawon, and Nieper-Wißkirchen.
 
Join Zoom Meeting:
Meeting ID: 947 8793 7855
Passcode: 323472


 

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