scholarly journals Perverse sheaves and Milnor fibers over singular varieties

2019 ◽  
Author(s):  
Kiyoshi Takeuchi
Keyword(s):  
Perverse Sheaves ◽  
Singular Varieties

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.

Explicit Models for Perverse Sheaves, II

2007 ◽  
Vol 11 (2) ◽  
pp. 149-178 ◽  
Author(s):  
F. Gudiel-Rodríguez ◽  
L. Narváez-Macarro
Keyword(s):  
Perverse Sheaves

Perverse sheaves on rank stratifications

1999 ◽  
Vol 96 (2) ◽  
pp. 317-362 ◽  
Author(s):  
Tom Braden ◽  
Mikhail Grinberg
Keyword(s):  
Perverse Sheaves

scholarly journals Vanishing theorems for perverse sheaves on abelian varieties, revisited

2017 ◽  
Vol 24 (1) ◽  
pp. 63-84 ◽  
Author(s):  
Bhargav Bhatt ◽  
Christian Schnell ◽  
Peter Scholze
Keyword(s):  
Abelian Varieties ◽  
Vanishing Theorems ◽  
Perverse Sheaves

Lightning Introduction to Perverse Sheaves

2020 ◽  
pp. 315-331
Author(s):  
Ben Elias ◽  
Shotaro Makisumi ◽  
Ulrich Thiel ◽  
Geordie Williamson
Keyword(s):  
Perverse Sheaves

scholarly journals Irregular perverse sheaves

2021 ◽  
Vol 157 (3) ◽  
pp. 573-624
Author(s):  
Tatsuki Kuwagaki
Keyword(s):  
Abelian Category ◽  
Derived Category ◽  
Perverse Sheaves ◽  
Algebraic Version ◽  
Constructible Sheaves ◽  
Straightforward Generalization ◽  
Novikov Ring

We introduce irregular constructible sheaves, which are ${\mathbb {C}}$-constructible with coefficients in a finite version of the Novikov ring $\Lambda$ and special gradings. We show that the bounded derived category of cohomologically irregular constructible complexes is equivalent to the bounded derived category of holonomic ${\mathcal {D}}$-modules by a modification of D’Agnolo and Kashiwara's irregular Riemann–Hilbert correspondence. The bounded derived category of cohomologically irregular constructible complexes is equipped with the irregular perverse $t$-structure, which is a straightforward generalization of usual perverse $t$-structure, and we prove that its heart is equivalent to the abelian category of holonomic ${\mathcal {D}}$-modules. We also develop the algebraic version of the theory.

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
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