Related papers: Complete intersections in spherical varieties

We prove the "Sullivan Conjecture" on the classification of 4-dimensional complete intersections up to diffeomorphism. Here an $n$-dimensional complete intersection is a smooth complex variety formed by the transverse intersection of $k$…

Let $M=G/H$ be a Riemannian homogeneous space, where $G$ is a compact Lie group with closed subgroup $H$. Classical intersection theory states that the de Rham cohomology ring of $M$ describes the signed count of intersection points of…

We prove the structure theorem of the intersection complexes of toric varieties in the category of mixed Hodge modules. This theorem is due to Bernstein, Khovanskii and MacPherson for the underlying complexes with rational coefficients. As…

Using Saito's theory of mixed Hodge modules, we study a generalization of Hellus-Schenzel's "cohomologically complete intersection" property. This property is equivalent to perversity of the shifted constant sheaf. We relate the generalized…

Let $K$ be a non-archimedean local field of residual characteristic $p\neq 2$. Let $G$ be a connected reductive group over $K$, let $\theta$ be an involution of $G$ over $K$, and let $H$ be the connected component of $\theta$-fixed subgroup…

Let $k_0$ be a field of characteristic $0$ with algebraic closure $k$. Let $G$ be a connected reductive $k$-group, and let $Y$ be a spherical variety over $k$ (a spherical homogeneous space or a spherical embedding). Let $G_0$ be a…

We describe a class of affine toric varieties $V$ that are set-theoretically minimally defined by codim $V+1$ binomial equations over fields of any characteristic.

Let $X$ be a quasi projective scheme over a noetherian affine scheme $Spec(A)$, $U\subseteq X$ be an open subset, and $Z=X-U$.Assume that $Z$ is complete intersection, with $k=codim Z$. Consider the map $$ q:{\mathbb K}\left({\mathscr…

Let G be a (real or complex) linear reductive algebraic group acting on an affine variety V. Let W be a subvariety. In this work we study how the G-orbits intersect W. We develop a criterion to determine when the intersection can be…

The main purpose of this paper is to define the {\it net logarithmic tangent sheaf}, as a generalization of the logarithmic tangent sheaf introduced by P.~Deligne, over the field of complex numbers, and prove some basic properties and give…

We present a full list of all representations of the special linear group $\mathrm{SL}_n$ over the complex numbers with complete intersection invariant ring, completing the classification of Shmelkin. For this task, we combine three…

We present a SageMath package for calculating elliptic genera of homogeneous spaces and their complete intersections. This includes the calculation of the basis of weak Jacobi forms, Chern numbers of homogeneous spaces and their complete…

We prove that if $G$ is a noncompact connected real reductive linear Lie group, then any discrete subgroup of $G$ acting properly discontinuously and cocompactly on some homogeneous space $G/H$ of $G$ is quasi-isometrically embedded and…

We define total Frobenius-Schur indicator for each object in a spherical fusion category $C$ as a certain canonical sum of its higher indicators. The total indicators are invariants of spherical fusion categories. If $C$ is the…

Let X be a normal projective Q-Gorenstein variety with at worst log-terminal singularities. We prove a formula expressing the total stringy Chern class of a generic complete intersection in X via the total stringy Chern class of X. This…

Given a non compact semisimple Lie group $G$ we describe all homogeneous spaces $G/L$ carrying an invariant almost K\"ahler structure $(\omega,J)$. When $L$ is abelian and $G$ is of classical type, we classify all such spaces which are…

Let $G=(V,E)$ be a finite, simple graph. We consider for each oriented graph $G_{\cal O}$ associated to an orientation ${\cal O}$ of the edges of $G$, the toric ideal $P_{G_{\cal O}}$. In this paper we study those graphs with the property…

Let $n$ be an even natural number. We compute the periods of any $\frac{n}{2}$-dimensional complete intersection algebraic cycle inside an $n$-dimensional non-degenerated intersection of a projective simplicial toric variety. Using this…

A linear connection on a Lie algebroid is called a Cartan connection if it is suitably compatible with the Lie algebroid structure. Here we show that a smooth connected manifold $M$ is locally homogeneous - i.e., admits an atlas of charts…

Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module of finite dimension. If G/H \subset P(V) is a spherical orbit and if X is its closure,…