Related papers: Weighted Chern-Mather classes and Milnor classes o…

We give a new proof of the classification due to Peternell-Szurek-Wi\'{s}niewski of nef vector bundles on a projective space with the first Chern class less than three and on a smooth hyperquadric with the first Chern class less than two…

In this article, we give numerical restrictions on the Chern classes of Ulrich bundles on higher-dimensional manifolds, which are inspired by the results of Casnati in the case of surfaces. As a by-product, we prove that the only projective…

We define integral geometric analogues of the Chern classes for real vector bundle on a smooth real variety. More precisely, we define the Chern densities of a real bundle. These densities are analogues of the Chern forms of a complex…

In this paper we study ACM vector bundles $\E$ of rank $k \geq 3$ on hypersurfaces $X_r \subset\Pj^4$ of degree $r \geq 1$. We consider here mainly the case of degree $r = 4$, which is the first unknown case in literature. Under some…

This paper continues our researches \cite{DS1, DS2, DS3} by computing some invariants based on Hilbert-Poincar\'{e} series associated to Milnor algebras. Our computations are for some of the classical surfaces and 3-folds with different…

We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on surfaces within the framework of Nakajima's oscillator algebra. This leads to an identification…

We prove an identity of Segre classes for zero-schemes of compatible sections of two vector bundles. Applications include bounds on the number of equations needed to cut out a scheme with the same Segre class as a given subscheme of (for…

We extend the Hirzebruch-Milnor class of a hypersurface $X$ to the case where the normal bundle is nontrivial and $X$ cannot be defined by a global function, using the associated line bundle and the graded quotients of the monodromy…

Let G be a complex connected reductive group. The representation ring R(G) admits a canonical filtration defined in terms of the lambda-structure. We compute the associated graded ring gr R(G) (over Q) and the Chern classes of a…

For a discrete group $\Gamma$, we study vector bundles $E_\rho$ on compact subsets of $B\Gamma$ associated to almost representations $\rho:\Gamma \to U(n)$. We compute the first Chern class of $E_\rho$ in terms of $\rho$. When $\rho$ is…

A relative Picard theory in the context of graded manifolds is introduced. A Berezinian calculus and a theory of connections over SUSY-curves are systematically developed, and used to prove a Gauss-Bonnet theorem for line bundles in that…

We show that Quillen's formalism for computing the Chern character of the index using superconnections extends to arbitrary operators with functional calculus. We thus remove the condition that the operators have, up to homotopy, a gap in…

In this series of lectures, I will discuss results for complex hypersurfaces with non-isolated singularities. In Lecture 1, I will review basic definitions and results on complex hypersurfaces, and then present classical material on the…

We extend the concept of Segre's Invariant to vector bundles on a surface $X$. For $X=\mathbb{P}^2$ we determine what numbers can appear as the Segre Invariant of a rank $2$ vector bundle with given Chern's classes. The irreducibility of…

We classify equivariant topological complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most)…

In the cohomology ring of an extraspecial p-group, the subring generated by Chern classes and transfers is studied. This subring is strictly larger than the Chern subring, but still not the whole cohomology ring, even modulo nilradical. A…

We prove two results about vector bundles on singular algebraic surfaces. First, on proper surfaces there are vector bundles of rank two with arbitrarily large second Chern number and fixed determinant. Second, on separated normal surfaces…

The goal of this work is to construct integral Chern classes and higher cycle classes for a smooth variety over a perfect field of characteristic p>0 that are compatible with the rigid Chern classes defined by Petrequin. The Chern classes…

Using monads, we construct a large class of stable bundles of rank 2 and 3 on 3-fold hypersurfaces, and study the set of all possible Chern classes of stable vector bundles.

Consider the blow up $\pi: \widetilde{X} \to X$ of a rational surface $X$ at a point. Let $\widetilde{V}$ be a holomorphic bundle over $\widetilde{X}$ whose restriction to the exceptional divisor equals ${\cal{O}(j) \oplus {\cal O}(-j)$ and…