Related papers: A secondary Chern-Euler class

In this work we prove that for a compact odd-dimensional orbifold its Euler characteristic is half of the Euler characteristic of its boundary.

Let $W$ be a finite group and $T$ be an abelian group. Consider an extension $0 \ra T \ra N \ra W \ra 0$. For a smooth projective curve $X$, we give a precise description of the fiber of the quotient by $T$ map $q_T: \cM_X(N) \ra \cM_X(W)$…

We present two formulas for Chern classes of the tensor product of two vector bundles. In the first formula we consider a matrix containing Chern classes of the first bundle and we take a polynomial of this matrix with Chern classes of the…

Let $K$ be an algebraically closed field of characteristic $0$. For $m\geq n$, we define $\tau_{m,n,k}$ to be the set of $m\times n$ matrices over $K$ with kernel dimension $\geq k$. This is a projective subvariety of $\bbP^{mn-1}$, and is…

We classify the irreducible components of the space of foliations on Fano 3-folds with rank one Picard group. As a corollary we obtain a classification of holomorphic Poisson structures on the same class of 3-folds.

We study in detail the underlying graded geometric structure of abelian N=2 supersymmetric Chern-Simons theory in $(2+1)$-dimensions. This structure is an attribute of the hidden unbroken one dimensional N=2 supersymmetries that the system…

When two smooth manifold bundles over the same base are fiberwise tangentially homeomorphic, the difference is measured by a homology class in the total space of the bundle. We call this the relative smooth structure class. Rationally and…

Let $X$ be a compact K\"ahler fourfold with klt singularities and vanishing first Chern class, smooth in codimension two. We show that $X$ admits a Beauville-Bogomolov decomposition: a finite quasi-\'etale cover of $X$ splits as a product…

We study the existence problem and the enumeration problem for sections of Serre fibrations over compact orientable surfaces. When the fundamental group of the fiber is finite, a complete solution is given in terms of 2-dimensional…

Let $ E \xrightarrow[\text{}]{\pi} B$ be an oriented circle bundle over an oriented closed surface $B$. A quasisection is a smooth surface ${Q}$ (either closed or bordered) mapped by a generic smooth mapping $q$ to $E$ such that $\pi\circ…

We consider an arbitrary linear elliptic first--order differential operator A with smooth coefficients acting between sections of complex vector bundles E,F over a compact smooth manifold M with smooth boundary N. We describe the analytic…

We show that a smooth projective non-degenerate arithmetically Cohen-Macaulay subvariety X of P^N infinite Cohen-Macaulay type becomes of finite Cohen-Macaulay type by removing Ulrich bundles if and only if N = 5 and X is a quartic scroll…

For the chiral oscillator described by a second order and degenerate Lagrangian with special Euclidean group of symmetries, we show, by cotangent bundle Hamiltonian reduction, that reduced equations are Lie-Poisson on dual of oscillator…

In this paper we give a formula for the Hirzebruch $\chi_y$-genus $\chi_y(X)$ and similarly for the motivic Hirzebruch class $T_{y*}(X)$ for possibly singular varieties $X$, using the Vandermonde matrix. Motivated by the notion of secondary…

Let $\pi\cln X\to \Delta^m$ be a proper smooth K\"ahler morphism from a complex manifold $X$ to the unit polydisc $\Delta^m$. Suppose the fibers over the complement of a proper analytic subset are biholomorphic to a fixed projective…

Let X be a smooth projective variety carrying an Ulrich bundle. In the first part of this note, we construct an Ulrich sheaf on n-th symmetric power of X, which is a singular variety when $DimX >1$. As a consequence, we get the existence of…

For a group $G$ of not prime power order, Oliver showed that the obstruction for a finite CW-complex $F$ to be the fixed point set of a contractible finite $G$-CW-complex is the Euler characteristic $\chi(F)$. He also has the similar…

We study a Hopf algebroid, $\calh$, naturally associated to the groupoid $U_n^\delta\ltimes U_n$. We show that classes in the Hopf cyclic cohomology of $\calh$ can be used to define secondary characteristic classes of trivialized flat…

In very rough terms, the main theorem is that the set, which consists of semistable vector bundles with trivial rational Chern classes and nontrivial kth cohomology on a smooth complex projective variety, is a degeneration of a union of…

Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and \xi a holomorphic line bundle on it such that r is not a divisor of degree(\xi). Let {\mathcal M}_\xi(r) denote the moduli space of stable…