Related papers: Stability of direct images under Frobenius morphis…

We consider slope stability of the canonical extension of the tangent bundle by the trivial line bundle and with the extension class c_1(T_X) on Picard-rank-1 Fano varieties. In cases where the index divides the dimension or the dimension…

We study the space of stability conditions $\Stab(X)$ on the non-compact Calabi-Yau threefold $X$ which is the total space of the canonical bundle of $\PP^2$. We give a combinatorial description of an open subset of $\Stab(X)$ and state a…

We give new sufficient conditions for the integrability and unique integrability of continuous tangent sub-bundles on manifolds of arbitrary dimension, generalizing Frobenius' classical Theorem for C^1 sub-bundles. Using these conditions we…

Let X be an irreducible smooth complex projective curve of genus g>2, and let x be a fixed point. A framed bundle is a pair (E,\phi), where E is a vector bundle over X, of rank r and degree d, and \phi:E_x\to C^r is a non-zero homomorphism.…

Let R be an integral domain of finite type over Z and let f:X --> Spec R be a smooth projective morphism of relative dimension d >= 1. We investigate, for a vector bundle E on the total space X, under what arithmetical properties of a…

Let $G$ be an almost simple simply-connected affine algebraic group over an algebraically closed field $k$ of characteristic $p > 0$. If $G$ has type $B_n$, $C_n$ or $F_4$, we assume that $p > 2$, and if $G$ has type $G_2$, we assume that…

Let (X,H) be a polarized smooth projective surface satisfying H^1(X,O_X)=0 and let F be either a rank one torsion-free sheaf or a rank two {\mu}H-stable vector bundle on X. Assume that c_1(F)/=0. In this article it is shown that the rank…

This article is the first one of a series of three articles devoted to direct images of isocrystals: here we consider isocrystals without Frobenius structure; in the second one (resp. the third one), we will introduce a Frobenius structure…

Let $X$ be a smooth, irreducible, projective algebraic surface, and let $\alpha \in \mathbb{Q}[m]_{>0}$ be a polynomial. In this paper, we determine topological and geometric properties of the moduli space of $\alpha$-stable coherent…

Let $f : X \rightarrow Y$ be a generically smooth nonconstant morphism between irreducible projective curves, defined over an algebraically closed field, which is \'etale on an open subset of $Y$ that contains both the singular locus of $Y$…

Let X be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that X does not have any real points. We classify the isomorphism classes of all stable real algebraic vector bundles over…

We use a recently proposed formulation of stable holomorphic vector bundles $V$ on elliptically fibered Calabi--Yau n-fold $Z_n$ in terms of toric geometry to describe stability conditions on $V$. Using the toric map $f: W_{n+1} \to…

We discuss the local freeness and the numerical semipositivity of direct images of relative pluricanonical bundles for surjective morphisms between smooth projective varieties with connected fibers. We give a desirable semipositivity…

We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo $p^2$ - we expect that such varieties, after a finite \'etale cover, admit a toric fibration over…

Given a quasi-projective scheme M over complex numbers equipped with a perfect obstruction theory and a morphism to a nonsingular quasi-projective variety B, we show it is possible to find an affine bundle M'/ M that admits a perfect…

Let X be an irreducible smooth projective curve, of genus at least two, over an algebraically closed field k. Let $\mathcal{M}^d_G$ denote the moduli stack of principal G-bundles over X of fixed topological type $d \in \pi_1(G)$, where G is…

We study the stability of the normal bundle of canonical genus $8$ curves and prove that on a general curve the bundle is stable. The proof rests on Mukai's description of these curves as linear sections of a Grassmannian $\mathrm{G}(2,6)$.…

In this paper, we prove that a smooth projective variety $X$ of characteristic $p>0$ is an ordinary abelian variety if and only if $K_X$ is pseudo-effective and $F^e_*\mathcal O_X$ splits into a direct sum of line bundles for an integer $e$…

Given varieties $X, Y, W$ and dominant morphisms $\phi:X\to Y$ and $f:X\to W$ such that $f$ is constant on fibres of $\phi$ , we give sufficient conditions to guarantee that $f$ descends to a rational map or a morphism $Y\to W.$ We pay…

Let $\pi:Y\to X$ be a surjective morphism between two irreducible, smooth complex projective varieties with ${\rm dim}Y>{\rm dim}X >0$. We consider polarizations of the form $L_c=L+c\cdot\pi^*A$ on $Y$, with $c>0$, where $L,A$ are ample…