Related papers: On degree zero semistable bundles over an elliptic…

We give the general presciption for calculating the moduli of irreducible, stable SU(n) holomorphic vector bundles with positive spectral covers over elliptically fibered Calabi-Yau threefolds. Explicit results are presented for Hirzebruch…

Geometric transitions between Calabi-Yau manifolds have proven to be a powerful tool in exploring the intricate and interconnected vacuum structure of string compactifications. However, their role in N=1, 4-dimensional string…

We show that the vector bundle on the moduli stack $M_\mathrm{ell}$ of elliptic curves associated to the $2$-cell complex $C\nu$ is isomorphic to the de Rham cohomology sheaf $\mathrm{H}^1_\mathrm{dR}(\mathcal{E}/M_\mathrm{ell})$ of the…

This paper studies a variant of Horrocks-type criteria for vector bundles mainly through a syzygy theoretic approach. Starting with explaining various proofs of the splitting criteria for ACM and Buchsbaum bundles, we are going to give new…

It has recently been realised that polystable, holomorphic sums of line bundles over smooth Calabi-Yau three-folds provide a fertile ground for heterotic model building. Large numbers of phenomenologically promising such models have been…

Studying degenerations of moduli spaces of semistable principal bundles on smooth curves leads to the problem of constructing and studying moduli spaces on singular curves. In this note, we will see that the moduli spaces of…

This paper primarily concerns the variance estimate of zeros of systems of random holomorphic sections associated with a sequence of smooth Hermitian holomorphic line bundles on a compact Kahler manifold X. The probability measures taken…

This paper presents the theory of holomorphic vector valued modular forms from a geometric perspective. More precisely, we define certain holomorphic vector bundles on the modular orbifold of generalized elliptic curves whose sections are…

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…

Let $M$ be a compact connected K\"ahler manifold and let ${\E}_{l-1}$ be the smallest term in the Harder-Narasimhan filtration of its tangent bundle. Let $G$ be an affine algebraic reductive group over $\C$. We prove the following result:…

We further develop the numerical algorithm for computing the gauge connection of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In particular, recent work on the generalized Donaldson algorithm is extended to bundles with…

It is in general unknown which topological complex vector bundles on a non-algebraic surface admit holomorphic structures. We solve this problem for primary Kodaira surfaces by using results of Kani on curves of genus two with elliptic…

We provide the methods to compute the complete massless spectra of a class of recently introduced supersymmetric E8 x E8 heterotic string models which invoke vector bundles with U(N) structure group on simply connected Calabi-Yau manifolds…

Koll\'{a}r showed that small deformations of elliptically fibered smooth $K$-torsion varieties with $H^2(X,\mathcal{O}_X)=0$ remain elliptically fibered. We extend this result to any fibered smooth $K$-torsion variety $X$ with…

A compact topological surface S, possibly non-orientable and with non-empty boundary, always admits a Klein surface structure (an atlas whose transition maps are dianalytic). Its complex cover is, by definition, a compact Riemann surface M…

We give an algebraic proof valid in arbitrary characteristic for the known equivalence between (strongly) slope semistable vector bundles with vanishing discriminant and vanishing determinant and numerically flat bundles. We also address a…

We adapt the notions of stability of holomorphic vector bundles in the sense of Mumford-Takemoto and Hermitian-Einstein metrics in holomorphic vector bundles for canonically polarized framed manifolds, i.e. compact complex manifolds X…

We extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we…

We systematically study the splitting of vector bundles on a smooth, projective variety, whose restriction to the zero locus of a regular section of an ample vector bundle splits. First, we find ampleness and genericity conditions which…

Let $(E,\varphi)$ be decorated vector bundle of type $(a,b,c,N)$ on a smooth projective curve $X$. There is a suitable semistability condition for such objects which has to be checked for any weighted filtration of $E$. We prove, at least…