scholarly journals On Singular Varieties Having an Extremal Secant Line

2006 ◽  
Vol 34 (3) ◽  
pp. 893-909 ◽  
Author(s):  
Marie-Amélie Bertin
Keyword(s):  
Singular Varieties ◽  
Secant Line

scholarly journals Geometry and topology of the space of Kähler metrics on singular varieties

2018 ◽  
Vol 154 (8) ◽  
pp. 1593-1632 ◽  
Author(s):  
Eleonora Di Nezza ◽  
Vincent Guedj
Keyword(s):  
Einstein Metrics ◽  
Normal Space ◽  
Fano Varieties ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Metric Properties ◽  
Singular Varieties ◽  
Underlying Space ◽  
And Topology ◽  
Kähler Einstein Metrics

Let $Y$ be a compact Kähler normal space and let $\unicode[STIX]{x1D6FC}\in H_{\mathit{BC}}^{1,1}(Y)$ be a Kähler class. We study metric properties of the space ${\mathcal{H}}_{\unicode[STIX]{x1D6FC}}$ of Kähler metrics in $\unicode[STIX]{x1D6FC}$ using Mabuchi geodesics. We extend several results of Calabi, Chen, and Darvas, previously established when the underlying space is smooth. As an application, we analytically characterize the existence of Kähler–Einstein metrics on $\mathbb{Q}$-Fano varieties, generalizing a result of Tian, and illustrate these concepts in the case of toric varieties.

scholarly journals Elliptic genera of singular varieties

2003 ◽  
Vol 116 (2) ◽  
pp. 319-351 ◽  
Author(s):  
Anatoly Libgober ◽  
Lev Borisov
Keyword(s):  
Singular Varieties ◽  
Elliptic Genera

scholarly journals Valuation spaces and multiplier ideals on singular varieties

2015 ◽  
pp. 29-51 ◽  
Author(s):  
S. Boucksom ◽  
T. de Fernex ◽  
C. Favre ◽  
S. Urbinati
Keyword(s):  
Multiplier Ideals ◽  
Singular Varieties
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