In this paper, we prove that for the oper stratification of de Rham moduli space $M_{\mathrm{dR}}(X,r)$, closed stratum is unique minimal with dimension $r^2(g-1)+g+1$, and open dense consisting irreducible flat bundles stable underlying vector maximal stratum.

Let X be a smooth projective algebraic curve of genus > 1 over and algebraically closed field k of characteristic p > 0. Denote by Bunn (resp. Locn) the moduli stack of vector bundles of rank n on X (resp. the moduli stack of vector bundles of rank n endowed with a connection). Let also DBunn denote the sheaf of crystalline differential operators on Bunn (cf. e.g. [3]). In this paper we constru...

Let X be a smooth projective algebraic curve of genus > 1 over and algebraically closed field k of characteristic p > 0. Denote by Bunn (resp. Locn) the moduli stack of vector bundles of rank n on X (resp. the moduli stack of vector bundles of rank n endowed with a connection). Let also DBunn denote the sheaf of crystalline differential operators on Bunn (cf. e.g. [3]). In this paper we constru...

We prove an analogue in higher dimensions of the classical Narasimhan-Seshadri theorem for strongly stable vector bundles with c1 = 0 on a smooth projective variety X . As applications, over fields of characteristic zero, we derive an effective version of the main theorem in a recent paper of Balaji and Kollár ([3]), and over uncountable fields of positive characteristics, if G is a semisimple ...

Homological mirror symmetry is a conjecture that a category constructed in the A-model and a category constructed in the B-model are equivalent in some sense. We construct a cyclic differential graded (DG) category of holomorphic vector bundles on noncommutative twotori as a category in the B-model side. We define the corresponding Fukaya’s category in the A-model side, and prove the equivalenc...

Let X be a smooth projective curve of genus g ≥ 2 over an algebraically closed field k of characteristic p > 0. Let MX be the moduli space of semistable rank-2 vector bundles over X with trivial determinant. The relative Frobenius map F : X → X1 induces by pull-back a rational map V : MX1 99K MX . In this paper we show the following results. (1) For any line bundle L over X , the rank-p vector ...

Let E be an elliptic curve over a field k. Let us denote by Vect(E) the category of algebraic vector bundles on E, where as space of morphisms from V1 to V2 we take the graded space Hom(V1, V2)⊕Ext (V1, V2) with the natural composition law. In this paper we study extensions of this (strictly associative) composition to A∞-structures on Vect(E) (see section 1 for the definition). The motivation ...