scholarly journals Cylinder deformations in orbit closures of translation surfaces

2015 ◽  
Vol 19 (1) ◽  
pp. 413-438 ◽  
Author(s):  
Alex Wright
Keyword(s):  
Translation Surfaces ◽  
Orbit Closures

scholarly journals Homogeneous orbit closures and applications

2011 ◽  
Vol 32 (2) ◽  
pp. 785-807 ◽  
Author(s):  
ELON LINDENSTRAUSS ◽  
URI SHAPIRA
Keyword(s):  
Real Number ◽  
Unit Volume ◽  
Orbit Closures ◽  
Image Position

AbstractWe give new classes of examples of orbits of the diagonal group in the space of unit volume lattices in ℝd for d≥3 with nice (homogeneous) orbit closures, as well as examples of orbits with explicitly computable but irregular orbit closures. We give Diophantine applications to the former; for instance, we show that, for all γ,δ∈ℝ, where 〈c〉 denotes the distance of a real number c to the integers.

Self-translation surfaces

1993 ◽  
Vol 5 (5) ◽  
Author(s):  
María del Carmen Fuster ◽  
Clin McGrory ◽  
Juan Ballesteros
Keyword(s):  
Translation Surfaces

Classification of higher rank orbit closures in ${\mathcal H^{\mathrm{odd}}(4)}$

2016 ◽  
Vol 18 (8) ◽  
pp. 1855-1872 ◽  
Author(s):  
David Aulicino ◽  
Duc-Manh Nguyen ◽  
Alex Wright
Keyword(s):  
Orbit Closures ◽  
Higher Rank

Weingarten Affine Translation Surfaces in Euclidean 3-Space

2017 ◽  
Vol 72 (4) ◽  
pp. 1839-1848 ◽  
Author(s):  
Seoung Dal Jung ◽  
Huili Liu ◽  
Yixuan Liu
Keyword(s):  
Translation Surfaces ◽  
Affine Translation

scholarly journals Poincaré polynomials of generic torus orbit closures in Schubert varieties

2021 ◽  
pp. 189-208
Author(s):  
Eunjeong Lee ◽  
Mikiya Masuda ◽  
Seonjeong Park ◽  
Jongbaek Song
Keyword(s):  
Schubert Variety ◽  
Flag Variety ◽  
Schubert Varieties ◽  
Orbit Closure ◽  
Poincaré Polynomial ◽  
Content Type ◽  
Eulerian Polynomial ◽  
Orbit Closures

The closure of a generic torus orbit in the flag variety G / B G/B of type  A A is known to be a permutohedral variety, and its Poincaré polynomial agrees with the Eulerian polynomial. In this paper, we study the Poincaré polynomial of a generic torus orbit closure in a Schubert variety in  G / B G/B . When the generic torus orbit closure in a Schubert variety is smooth, its Poincaré polynomial is known to agree with a certain generalization of the Eulerian polynomial. We extend this result to an arbitrary generic torus orbit closure which is not necessarily smooth.

scholarly journals The Kontsevich–Zorich cocycle over Veech–McMullen family of symmetric translation surfaces

2019 ◽  
Vol 14 (1) ◽  
pp. 21-54
Author(s):  
Artur Avila ◽  
◽  
Carlos Matheus ◽  
Jean-Christophe Yoccoz ◽  
◽  
...  
Keyword(s):  
Translation Surfaces
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