Related papers: Syzygies using vector bundles

This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…

We study iterations of two classical constructions, the evolutes and involutes of plane curves, and we describe the limiting behavior of both constructions on a class of smooth curves with singularities given by their support functions.…

A linear connection is associated to a nonlinear connection on a vector bundle by a linearization procedure. Our definition is intrinsic in terms of vector fields on the bundle. For a connection on an affine bundle our procedure can be…

Let $(X,L)$ be a polarized smooth projective variety. For any basepoint-free linear system $\mathcal{L}_{V}$ with $V\subset H^{0}(X,\mathcal{O}_{X}(L))$ we consider the syzygy bundle $M_{V}$ as the kernel of the evaluation map $V\otimes…

A first step towards a systematic theory of relative line bundles over SUSY-curves is presented. In this paper we deal with the case of relative line bundles over families of ordinary Riemann surfaces. Generalizations of the Gauss-Bonnet…

Let $X$ be a K3 surface and let $\text{Spl}(r;c_1,c_2)$ be the moduli space of simple sheaves on $X$ of fixed rank $r$ and Chern classes $c_1$ and $c_2$. Under suitable assumptions, to a pair $(F,W)$ (respectively, $(F,V)$) where $F\in…

We survey results concerning behavior of positivity of line bundles and possible vanishing theorems in positive characteristic. We also try to describe variation of positivity in mixed characteristic. These problems are very much related to…

The dimension of spaces of global sections for line bundles on semistable curves parametrized by the compactified Picard scheme is studied. The theorem of Riemann is shown to hold. The theorem of Clifford is shown to hold in the following…

The aim of this paper is to give some characterizations for N-Legendre and N-slant curves in the unit tangent bundles of surfaces endowed with natural diagonal lifted structures.

From a certain strongly equivariant bundle gerbe with connection and curving over a smooth manifold on which a Lie group acts, we construct under some conditions a bundle gerbe with connection and curving over the quotient space. In…

Given a vector bundle $F$ on a variety $X$ and $W\subset H^0(F)$ such that the evaluation map $W\otimes \mathcal{O}_X\to F$ is surjective, its kernel $S_{F,W}$ is called generalized syzygy bundle. Under mild assumptions, we construct a…

We extend our previous theory of etale parallel transport to a larger class of slope zero vector bundles on p-adic curves. The new class is stable under pullback by ramified coverings. We also construct p-adic representations of a central…

We investigate the analog of holomorphic vector bundles in the context of Sasakian manifolds.

In this article, the existence of Ulrich bundles on projective bundles $\mathbb P(E) \to X$ is discussed. In the case, that the base variety $X$ is a curve or surface, a close relationship between Ulrich bundles on $X$ and those on $\mathbb…

In this paper we state and prove some results on the structure of the jetbundles as left and right module over the structure sheaf on the projective line and projective space using elementary techniques involving diagonalization of…

Jet manifolds and vector bundles allow one to employ tools of differential geometry to study differential equations, for example those arising as equations of motions in physics. They are necessary for a geometrical formulation of…

Let $L$ be a (semi)-positive line bundle over a Kahler manifold, $X$, fibered over a complex manifold $Y$. Assuming the fibers are compact and non-singular we prove that the hermitian vector bundle $E$ over $Y$ whose fibers over points $y$…

We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we give applications in the studies of the…

In previous papers it was shown that the left and right O-module structure of the jet bundles on the projective line differed. In this paper we show that similar statements hold for jet bundles on projective space in any dimension. We also…

Given two arbitrary vector bundles on the Fargues-Fontaine curve, we completely classify all vector bundles which arise as their extensions.