Related papers: Descent of line bundles to GIT quotients of flag v…

We consider the descent of line bundles to GIT quotients of products of flag varieties. Let $G$ be a simple, connected, algebraic group over $\mathbb{C}$. We fix a Borel subgroup $B$ and consider the diagonal action of $G$ on the projective…

Let $G=SL_n(\mathbb C)$ and $T$ be a maximal torus in $G$. We show that the quotient $T \backslash \backslash G/{P_{\alpha_1}\cap P_{\alpha_2}}$ is projectively normal with respect to the descent of a suitable line bundle, where…

Let $k$ be an algebraically closed field. Consider a reductive group $G$ over $k$. Let $X$ be a projective variety over $k$ with a $G$-action and let $L$ be a very ample $G$-linearized line bundle on $X$. Suppose that $L$ descends to the…

In this paper we investigate line bundles on $\mathrm{Bun}_{\mathcal{G}}$ the moduli stack of parahoric Bruhat--Tits bundles over a smooth projective curve. Translating this problem into one concerning twisted conformal blocks, we are able…

Let $X$ be flat scheme over $\mathbb{Z}$ such that its base change, $X_p$, to $\bar{\mathbb{F}}_p$ is Frobenius split for all primes $p$. Let $G$ be a reductive group scheme over $\mathbb{Z}$ acting on $X$. In this paper, we prove a result…

We give a stratification of the GIT quotient of the Grassmannian $G_{2,n}$ modulo the normaliser of a maximal torus of $SL_{n}(k)$ with respect to the ample generator of the Picard group of $G_{2,n}$. We also prove that the flag variety…

For any simple, simply connected algebraic group $G$ of type $B,C$ and $D$ and for any maximal parabolic subgroup $P$ of $G$, we provide a criterion for a Richardson variety in $G/P$ to admit semistable points for the action of a maximal…

We study a variation of Mumford's quotient for the action of a maximal torus $T$ on a flag variety $G/B$ depending on projective embedding $G/B \hookrightarrow \Bbb P(V(\chi))$, where $T$-linearization is induced by the standard…

Let $r$ and $q$ be positive integers and $n=qr+1.$ Let $G = SL(n, \mathbb{C})$ and $T$ be a maximal torus of $G.$ Let $P^{\alpha_r}$ be the maximal parabolic subgroup of $G$ corresponding to the simple root $\alpha_r.$ Let $\omega_r$ be the…

Let G be a connected complex semi-simple group, B a Borel subgroup of G, and T a maximal torus in B. We construct a class of smooth T-stable subvarieties inside the flag variety G/B, each of which is an embedding of a product of projective…

In this paper, we develop a theory of Galois descent for equivariant line bundles on partial flag schemes. In particular, we study computational aspects of the classification of descent data of equivariant line bundles attached to…

Let $G$ be a simple algebraic group of adjoint type of rank $n$ over $\mathbb{C}$. Let $T$ be a maximal torus of $G$, and $B$ be a Borel subgroup of $G$ containing $T$. Let $W=N_{G}(T)/T$ be the Weyl group of $G$. Let…

In this paper, we consider the GIT quotients of Schubert varieties for the action of a maximal torus. We describe the minuscule Schubert varieties for which the semistable locus is contained in the smooth locus. As a consequence, we study…

Let $X$ be a complex toric variety equipped with the action of an algebraic torus $T$, and let $G$ be a complex linear algebraic group. We classify all $T$-equivariant principal $G$-bundles $\mathcal{E}$ over $X$ and the morphisms between…

Let $G$ be a connected linear algebraic group over a field $k$ of characteristic zero. For a principal $G$-bundle $\pi: E \to X$ over a scheme $X$ of finite type over $k$ and a parabolic subgroup $P$ of $G$, we describe the rational…

Let P be a parabolic subgroup of a semisimple complex Lie group G defined by a subset \Sigma of simple roots of G, and let E_\phi be a homogeneous vector bundle over the flag manifold G/P corresponding to a linear representation \phi of P.…

Let $k$ be an algebraically closed field of characteristic $p\neq 0$. Let $G$ be a connected reductive group over $k$, $P \subseteq G$ be a parabolic subgroup and $\lambda: P \longrightarrow \mathbb G_m$ be a strictly anti-dominant…

We consider topological T-duality of torus bundles equipped with S^{1}-gerbes. We show how a geometry on the gerbe determines a reduction of its band to the subsheaf of S^{1}-valued functions which are constant along the torus fibres. We…

Let C be a smooth projective curve with genus g>1 and Clifford index c(C) and let L be a line bundle on C generated by its global sections. The morphism i:C -->P(H^0(L))=P is well-defined and i*T is the restriction to C of the tangent…

We determine some classes of varieties X - that include the varieties with numerically effective tangent bundle - satisfying the following property: if E is a Higgs bundle such that f*E is semistable for any morphism f from a smooth…