Related papers: Bundles on caudate curves

We classify (semi)stable sheaves on a rational curve with one node. The results are based on the classification of indecomposable torsion-free sheaves due to Drozd and Greuel "Tame and wild projective curves and classification of vector…

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 $\mathrm{G}(2,6)$.…

We define formal orbifolds over an algebraically closed field of arbitrary characteristic as curves together with some branch data. Their \'etale coverings and their fundamental groups are also defined. These fundamental group approximates…

Given a generically smooth stable curve over a discrete valuation ring such that its special fibre is irreducible with one double point, we construct a moduli stack over that descrete valuation ring which is a model for the moduli stack of…

Given a connected reductive algebraic group G, we investigate the Picard group of the moduli stack of principal G-bundles over an arbitrary family of smooth curves.

Let $C$ be a comb-like curve over $\mathbb{C}$, and $E$ be a vector bundle of rank $n$ on $C$. In this paper, we investigate the criteria for the semistability of the restriction of $E$ onto the components of $C$ when $E$ is given to be…

In this paper we characterize smooth complex projective varieties that admit a quadric bundle structure on some dense open subset in terms of the geometry of certain families of rational curves.

We study the connection between the generation of a fat point scheme supported at general points in the plane and the behaviour of the cotangent bundle with respect to some rational curves particularly relevant for the scheme. We put…

Generalized are the investigated in other works of the author transports along paths in fibre bundles to transports along arbitrary maps in them. Their structure and some properties are studied. Special attention is paid to the linear case…

We study the moduli stacks of real vector bundles of fixed rank and degree on a type I real algebraic curve and determine its mod 2 cohomology algebra in terms of characteristic classes.

We introduce tropical vector bundles, morphisms and rational sections of these bundles and define the pull-back of a tropical vector bundle and of a rational section along a morphism. Afterwards we use the bounded rational sections of a…

We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools from analytic number theory.

We describe a technique for bundled curve representations in parallel-coordinates plots and present a controlled user study evaluating their effectiveness. Replacing the traditional C^0 polygonal lines by C^1 continuous piecewise Bezier…

For smooth projective curves the Clifford index is an important invariant which provides a bound for the dimension of the space of sections of a line bundle. This is the first step in distinguishing curves of the same genus. In this paper…

Let $E$ be a vector bundle on a curve $C$ of compact type and $V \subseteq \mathrm{H}^0(C, E)$ be a linear subspace that generates $E$. In this note, we study the stability of the syzygy bundle $M_{E,V}$ associated to $(E, V )$ over certain…

We prove that the moduli spaces of framed bundles over a smooth projective curve are rational. We compute the Brauer group of these moduli spaces to be zero under some assumption on the stability parameter.

We investigate topological properties of torsors in algebraic geometry over adelic rings.

We study quotients of multi-graded bundles, including double vector bundles. Among other things, we show that any such quotient fits into a tower of affine bundles. Applications of the theory include a construction of normal bundles for…

We give an algorithm for calculating the splitting type of the normal bundle of any rational monomial curve. The algorithm is obtained by reducing the calculus to a combinatorial problem and then by solving this problem.

Here we study vector bundles $E$ on the Hirzebruch surface $F_e$ such that their twists by a spanned, but not ample, line bundle $M = \mathcal {O}_{F_e}(h+ef)$ have natural cohomology, i.e. $h^0(F_e,E(tM)) >0$ implies $h^1(F_e,E(tM)) = 0$.