Related papers: Singularity Classes of Special 2-Flags

In the classification of real singularities by Arnold et al. (1985), normal forms, as representatives of equivalence classes under right equivalence, are not always uniquely determined. We describe the complete structure of the equivalence…

We define degeneracy loci for vector bundles with structure group $G_2$, and give formulas for their cohomology (or Chow) classes in terms of the Chern classes of the bundles involved. When the base is a point, such formulas are part of the…

We introduce the concept of a graded bundle which is a natural generalization of the concept of a vector bundle and whose standard examples are higher tangent bundles T^nQ playing a fundamental role in higher order Lagrangian formalisms.…

In this paper we provide sufficient conditions for maps of vector bundles on smooth projective varieties to be uniquely determined by their degeneracy schemes. We then specialize to holomorphic distributions and foliations. In particular,…

Given a smooth totally nonholonomic distribution on a smooth manifold, we construct a singular distribution capturing essential abnormal lifts which is locally generated by vector fields with controlled divergence. Then, as an application,…

We study several subseries of the space of second order theta functions on the Jacobian of a non-hyperelliptic curve. In particular, we are interested in the subseries P\Gamma_{00} consisting of 2theta-divisors having multiplicity at least…

For a 2-category 2C we associate a notion of a principal 2C-bundle. In case of the 2-category of 2-vector spaces in the sense of M.M. Kapranov and V.A. Voevodsky this gives the the 2-vector bundles of N.A. Baas, B.I. Dundas and J. Rognes.…

Motivated by the geometric theory of differential equations and the variational approach to the equivalence problem for geometric structures on manifolds, we consider the problem of equivalence for distributions with fixed submanifolds of…

In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that 1-jet of a vector bundle carries two vector bundle structures, namely…

The geometric theory of pseudo-differential and Fourier Integral Operators relies on the symplectic structure of cotangent bundles. If one is to study calculi with some specific feature adapted to a geometric situation, the corresponding…

We consider the question whether an orientable 5-manifold can be equipped with a rank two distribution of Cartan type and what 2-plane bundles can be realized. We obtain a complete answer for open manifolds. In the closed case, we settle…

The purpose of this present paper is to investigate the geometric structure of regular overdetermined systems of second order with two independent and one dependent variables from the point of view of rank 2 prolongations. Utilizing this…

A 2-web in the plane is given by two everywhere transverse 1-foliations. In this paper we introduce the study of singular 2-webs, given by any two foliations, which may be tangent in some points. We show that such two foliations are tangent…

This paper introduces four matrix normal distributions on analytic bundles of flag varieties, extending the separable covariance $\varPhi \otimes \varPsi$ with potentially variable-level ($\varPsi$) and/or sample-level ($\varPhi$)…

Farkas and Ortega found counterexamples to Mercat's conjecture by restricting to a hyperplane section $C$ some suitable rank-two vector bundles on a $K3$ surface whose Picard group is generated by $C$ and another very ample divisor. We…

Fold maps are fundamental tools in the theory of singularities of differentiable maps and its applications to geometry. They are higher dimensional variants of Morse functions. Classes of special generic maps and round fold maps are…

We consider links of complex isolated hypersurface singularities in $\mathbb{C}^{n+1}$ and study differentiable maps defined by restricting holomorphic functions to the links. We give an explicit example in which such a restriction gives a…

We define flag structures on a real three manifold M as the choice of two complex lines on the complexified tangent space at each point of M. We suppose that the plane field defined by the complex lines is a contact plane and construct an…

In this paper, we give a full description of all possible singular points that occur in generic 2-parameter families of vector fields on compact 2-manifolds. This is a part of a large project aimed to a complete study of global bifurcations…

Two new classes of metrizable vector bundles have been presented in the papers [1] and [4]. The Lie algebroid generalized tangent bundle of a dual vector bundle is presented. This Lie algebroid is a new example of metrizable vector bundle.…