A comb of origami curves in the moduli space M_3 with three dimensional closure

The Galois action on M-Origamis and their Teichmüller curves

We consider a rather special class of translation surfaces (called M-Origamis in this work) that are obtained from dessins by a construction introduced by Martin Möller. We give a new proof with a more combinatorial flavour of Möller's theorem that $\mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ acts faithfully on the Teichmüller curves of M-Origamis and extend his result by investigating the Galois action in greater detail. We determine the Strebel directions and corresponding cylinder decompositions of an M-Origami, as well as its Veech group, which contains the modular group $Γ(2)$ and is …

Closure relations for totally nonnegative cells in G/P

The totally nonnegative part of a partial flag variety G/P is known to have a decomposition into semi-algebraic cells. We show that the closure of a cell is again a union of cells and give a combinatorial description of the closure relations. The totally nonnegative cells are defined by intersecting the totally nonnegative part with a certain stratification of G/P defined by Lusztig. We also verify the same closure relations for these strata.

Simple Modules of Classical Linear Groups with Normal Closures of Maximal Torus Orbits

Let T be a maximal torus in a classical linear group G. In this paper we find all simple rational G-modules V such that for each vector v in V the closure of its T-orbit is a normal affine variety. For every other G-module we present a T-orbit with the non-normal closure. We use a combinatorial criterion of normality formulated in terms of the set of weights of a simple G-module. This work is a continuation of the previous work, where the same problem was solved in the case G=SL(n).

Normality of closure of orthogonal nilpotent symmetric orbits

We study closures of conjugacy classes in the symmetric matrices of the orthogonal group and we determine which one are normal varieties. In contrast to the result for the symplectic group where all classes have normal closure, there is only a relatively small portion of classes with normal closure. We perform a combinatorial computation on top of the same methods used by Kraft-Procesi and Ohta.

Simple Modules of Exceptional Groups with Normal Closures of Maximal Torus Orbits

Let G be an exceptional simple algebraic group, and let T be a maximal torus in G. In this paper, for every such G, we find all simple rational G-modules V with the following property: for every vector v in V, the closure of its T-orbit is a normal affine variety. For all G-modules without this property we present a T-orbit with the non-normal closure. To solve this problem, we use a combinatorial criterion of normality formulated in the terms of weights of a simple G-module. This paper continues two papers of the second author, where the same problem was solved for classical linear groups.

不可约特征环对于对称子群轨道闭包的研究

Irreducible Characteristic Cycles for Orbit Closures of a Symmetric Subgroup

本文研究了对称子群K在旗流形X上的轨道闭包的几何结构，证明了这些闭包具有不可约特征环，并通过局部化计算了其Chern-Mather类。