scholarly journals Connected components of the moduli spaces of Abelian differentials with prescribed singularities

2003 ◽  
Vol 153 (3) ◽  
pp. 631-678 ◽  
Author(s):  
Maxim Kontsevich ◽  
Anton Zorich
Keyword(s):  
Moduli Spaces ◽  
Connected Components ◽  
Abelian Differentials

scholarly journals Correction to: Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials

2021 ◽  
Author(s):  
Dawei Chen ◽  
Martin Möller ◽  
Adrien Sauvaget ◽  
Don Zagier
Keyword(s):  
Moduli Spaces ◽  
Intersection Theory ◽  
Abelian Differentials

A Correction to this paper has been published: https://doi.org/10.1007/s00222-020-00969-4

scholarly journals On Some Generalized Rapoport–Zink Spaces

2019 ◽  
Vol 72 (5) ◽  
pp. 1111-1187
Author(s):  
Xu Shen
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
K3 Surfaces ◽  
Connected Components ◽  
Shimura Varieties ◽  
Reductive Groups ◽  
Mixed Characteristic ◽  
Special Fibers ◽  
Type Spaces ◽  
Local Invariants

AbstractWe enlarge the class of Rapoport–Zink spaces of Hodge type by modifying the centers of the associated $p$-adic reductive groups. Such obtained Rapoport–Zink spaces are said to be of abelian type. The class of Rapoport–Zink spaces of abelian type is strictly larger than the class of Rapoport–Zink spaces of Hodge type, but the two type spaces are closely related as having isomorphic connected components. The rigid analytic generic fibers of Rapoport–Zink spaces of abelian type can be viewed as moduli spaces of local $G$-shtukas in mixed characteristic in the sense of Scholze.We prove that Shimura varieties of abelian type can be uniformized by the associated Rapoport–Zink spaces of abelian type. We construct and study the Ekedahl–Oort stratifications for the special fibers of Rapoport–Zink spaces of abelian type. As an application, we deduce a Rapoport–Zink type uniformization for the supersingular locus of the moduli space of polarized K3 surfaces in mixed characteristic. Moreover, we show that the Artin invariants of supersingular K3 surfaces are related to some purely local invariants.

scholarly journals Iterated double covers and connected components of moduli spaces

Topology ◽  
1997 ◽  
Vol 36 (3) ◽  
pp. 745-764 ◽  
Author(s):  
Marco Manetti
Keyword(s):  
Moduli Spaces ◽  
Connected Components ◽  
Double Covers

scholarly journals Faithful actions of the absolute Galois group on connected components of moduli spaces

2014 ◽  
Vol 199 (3) ◽  
pp. 859-888 ◽  
Author(s):  
Ingrid Bauer ◽  
Fabrizio Catanese ◽  
Fritz Grunewald
Keyword(s):  
Galois Group ◽  
Moduli Spaces ◽  
Connected Components ◽  
Absolute Galois Group ◽  
The Absolute

scholarly journals Connected components of moduli spaces

1986 ◽  
Vol 24 (3) ◽  
pp. 395-399 ◽  
Author(s):  
F. Catanese
Keyword(s):  
Moduli Spaces ◽  
Connected Components

scholarly journals On Selberg’s eigenvalue conjecture for moduli spaces of abelian differentials

2019 ◽  
Vol 155 (12) ◽  
pp. 2354-2398
Author(s):  
Michael Magee
Keyword(s):  
Moduli Spaces ◽  
Natural Extension ◽  
Abelian Differentials

J.-C. Yoccoz proposed a natural extension of Selberg’s eigenvalue conjecture to moduli spaces of abelian differentials. We prove an approximation to this conjecture. This gives a qualitative generalization of Selberg’s $\frac{3}{16}$ theorem to moduli spaces of abelian differentials on surfaces of genus ${\geqslant}2$.

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