Related papers: Birational geometry for nilpotent orbits

We give a geometric classification of $n$-dimensional nilpotent, commutative nilpotent and anticommutative nilpotent algebras. We prove that the corresponding geometric varieties are irreducible, find their dimensions and describe explicit…

This is a survey of the geometry of complex cubic fourfolds with a view toward rationality questions. Topics include classical constructions of rational examples, Hodge structures and special cubic fourfolds, associated K3 surfaces and…

This paper constructs a Riemann surface associated to the icosahedron and discusses the geodesics associated to a flat metric on this surface. Because of the icosahedral symmetry, this is a distinguished special case of the example treated…

The index of a Lie algebra is an important invariant which arises in several areas, e.g. in the study of coadjoint orbits for a Lie group, in invariant theory and in representation theory. We study the index for several classes of nilpotent…

In this manuscript, we compute explicitly the Lusztig-Vogan bijection for local systems of some classical, special, nilpotent orbits. Using these results, we prove a conjecture of Achar and Sommers on regular functions of some covers of…

We study the action of a nilpotent group G with finite generating set S on its horofunction boundary. We show that there is one finite orbit associated to each facet of the polytope obtained by projecting S into the infinite component of…

We investigate the birational geometry (in the sense of Mori's program) of the moduli space of rank 2 semistable parabolic vector bundles on a rational curve. We compute the effective cone of the moduli space and show that all birational…

We discuss the resolution of toroidal orbifolds. For the resulting smooth Calabi-Yau manifolds, we calculate the intersection ring and determine the divisor topologies. In a next step, the orientifold quotients are constructed.

In this paper we describe a multiparameter deformation of the function algebra of a semisimple coadjoint orbit. In the first section we use the representation of the Lie algebra on a generalized Verma module to quantize the Kirillov bracket…

We survey recent developments in the Birational Anabelian Geometry program aimed at the reconstruction of function fields of algebraic varieties over algebraically closed fields from pieces of their absolute Galois groups.

In this paper we consider non-compact non-complex exceptional Lie algebras, and compute the dimensions of the second cohomology groups for most of the nilpotent orbits. For the rest of cases of nilpotent orbits, which are not covered in the…

We study modules over stacks of deformation quantization algebroids on complex Poisson manifolds. We prove finiteness and duality theorems in the relative case and construct the Hochschild class of coherent modules. We prove that this class…

We study the moduli space of four dimensional ordinary Lie algebras, and their versal deformations. Their classification is well known; our focus in this paper is on the deformations, which yield a picture of how the moduli space is…

In this paper, we compute the character formula of the Brylinski model for all classical nilpotent varieties $\overline{\mathcal{O}}$. As a consequence, one can compute the multiplicities of all $K-$types of the ring of regular functions…

We study the quasi-admissibility and raisablility of some nilpotent orbits of a covering group. In particular, we determine the degree of the cover such that a given split nilpotent orbit is quasi-admissible and non-raisable. The speculated…

We study geometric properties of varieties associated with invariant subspaces of nilpotent operators. There are reductive algebraic groups acting on these varieties. We give dimensions of orbits of these actions. Moreover, a combinatorial…

We present twelve numerical methods for evaluation of objects and concepts from Poisson geometry. We describe how each method works with examples, and explain how it is executed in code. These include methods that evaluate Hamiltonian and…

Geometric Invariant Theory (GIT) produces quotients of algebraic varieties by reductive groups. If the variety is projective, this quotient depends on a choice of polarisation; by work of Dolgachev-Hu and Thaddeus, it is known that two…

In the context of affine complex Kac-Moody algebras, we define the meaning of nilpotent orbits under the adjoint action of the maximal Kac-Moody group. We also give a parameterization of nilpotent orbits of $\mathfrak{sl}_n^{(1)}(\mathbb…

We compute the equivariant fundamental class of the orbit closure of a linear series on the projective line. We also describe the boundary of the orbit closure and how the orbits specialise in one parameter families.