Related papers: Local Euler Obstruction and Chern-Mather classes o…

We show that every bad orbifold vector bundle can be realized as the restriction of a good orbifold vector bundle to a suborbifold of the base space. We give an explicit construction of this result in which the Chen-Ruan orbifold cohomology…

This paper continues the authors' work on the question of unitary equivalence of matrices with entries in the complex-valued functions of a topological space (matrices over spaces). Specifically, we here consider the question of unitary…

The ABCT variety is defined as the closure of the image of $G(2,n)$ under the Veronese map. We realize the ABCT variety $V(3,n)$ as the determinantal variety of a vector bundle morphism. We use this to give a recursive formula for the…

We consider compact homogeneous spaces G/H of positive Euler characteristic endowed with an invariant almost complex structure J and the canonical action \theta of the maximal torus T ^{k} on G/H. We obtain explicit formula for the…

We consider the scheme $X_{r,d,n}$ parametrizing $n$ ordered points in projective space $\mathbb{P}^r$ that lie on a common hypersurface of degree $d$. We show that this scheme has a determinantal structure and we prove that it is…

The focus of this paper is on a poorly understood invariant of a commutative noetherian local ring $R$ with residue field $k$: the stable cohomology modules $\hat{Ext}^{n}_R(k,k)$, defined for each $n\in\mathbb{Z}$ by Benson and Carlson,…

Roughly speaking, to any space $M$ with perfect obstruction theory we associate a space $N$ with symmetric perfect obstruction theory. It is a cone over $M$ given by the dual of the obstruction sheaf of $M$, and contains $M$ as its zero…

We prove homology stability for elementary and special linear groups over rings with many units improving known stability ranges. Our result implies stability for unstable Quillen K-groups and proves a conjecture of Bass. For commutative…

We establish a close connection between intersection multiplicities of special cycles on arithmetic models of the Shimura variety for GU(1,2) and Fourier coefficients of derivatives of certain incoherent Eisenstein series, confirming a…

We study the twisted K-theory and K-homology of some infinite dimensional spaces, like SU(\infty), in the bivariant setting. Using a general procedure due to Cuntz we construct a bivariant K-theory on the category of separable…

We propose and study the following Mirror Principle: certain sequences of multiplicative equivariant characteristic classes on Kontsevich's stable map moduli spaces can be computed in terms of certain hypergeometric type classes. As…

By the work of J.Huh, one can interpret binomial coefficients as a solution to an intersection problem on a permutohedral variety $X_E$. Applying Hirzebruch-Riemann-Roch, this intersection problem is equivalent to computing Euler…

We study moduli spaces of vector bundles on a two-dimensional neighbourhood $Z_k$ of an irreducible curve $\ell = CP^1$ with $\ell^2 = -k$ and give an explicit construction of these moduli as stratified spaces. We give sharp bounds for the…

Let $(X,0)$ be the germ of an equidimensional analytic set in $(\mathbb C^n,0)$ and $f=(f_1,f_2)$ a map-germ into the plane defined on $X.$ In this work, we investigate topological invariants associated to the pair $(f,X),$ among them, the…

Given a topological modular functor $\mathcal{V}$ in the sense of Walker \cite{Walker}, we construct vector bundles over $\bar{\mathcal{M}}_{g,n}$, whose Chern classes define semi-simple cohomological field theories. This construction…

We study intersection theory on the relative Hilbert scheme of a family of nodal-or-smooth curves, over a base of arbitrary dimension. We introduce an additive group called 'discriminant module', generated by diagonal loci, node scrolls,…

We prove that a general determinantal hypersurface of dimension 3 is nodal. Moreover, in terms of Chern classes associated with bundle morphisms, we derive a formula for the intersection homology Euler characteristic of a general…

In this paper, we consider an obstruction-theoretical construction of characteristic classes of fiber bundles by simplicial method. We can get a certain obstruction class for a deformation of $C_\infty$-algebra models of fibers and a…

We define the notion of a trace kernel on a manifold M. Roughly speaking, it is a sheaf on M x M for which the formalism of Hochschild homology applies. We associate a microlocal Euler class to such a kernel, a cohomology class with values…

This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our first main result is a family of sharp Chern class inequalities.…