Related papers: On intersection indices of subvarieties in reducti…

Let $P$ be a set of $n$ points in the plane, and let $\mathcal C$ be a collection of $n$ simple $k$-intersecting curves, meaning that every two distinct curves of $\mathcal C$ meet in at most $k$ points. A classical theorem of Pach and…

We study natural families of d-bar operators on the moduli space of stable parabolic vector bundles. Applying a families index theorem for hyperbolic cusp operators from our previous work, we find formulae for the Chern characters of the…

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…

Given a Hermitian holomorphic vector bundle over a complex manifold, consider its flag bundles with the associated universal vector bundles endowed with the induced metrics. We prove that the universal formula for the push-forward of a…

Differently from the Milnor number, no formula relating the Tjurina number of a reducible algebroid curve to invariants of its branches was known. The aim of this work is to provide such a formula for a complete intersection algebroid curve…

We introduce spectral Hirzebruch-Milnor classes for singular hypersurfaces. These can be identified with Steenbrink spectra in the isolated singularity case, and may be viewed as their global analogues in general. Their definition uses…

We find an algorithm to compute the quadratic Euler characteristic of a smooth projective complete intersection of hypersurfaces of the same degree. As an example, we compute the quadratic Euler characteristic of a smooth projective…

We compute superconformal indices for $\mathcal{N} = 3$ $\hat{ADE}$ Chern-Simons quiver gauge theories with a product gauge group $\prod_i U(N)_i$, using the method of supersymmetric localization. We also perform a large $N$ analysis of the…

We give an elementary proof of the fact that a pure-dimensional closed subvariety of a complex abelian variety has a signed intersection homology Euler characteristic. We also show that such subvarieties which, moreover, are local complete…

In this paper, we show the fundamental theorems for rotationally symmetric hypersurfaces, and thus, together with the earlier results in [3] and [4], provide a complete classification of umbilic hypersurfaces in the Heisenberg groups…

This paper studies intersection theory on the compactified moduli space M(n,d) of holomorphic bundles of rank n and degree d over a fixed compact Riemann surface of genus g > 1 where n and d may have common factors. Because of the presence…

In this paper we deal with some problems concerning minimal hypersurfaces in Carnot-Caratheodory (CC) structures. More precisely we will introduce a general calibration method in this setting and we will study the Bernstein problem for…

The classification of bandstructures by topological invariants provides a powerful tool for understanding phenomena such as the quantum Hall effect. This classification was originally developed in the context of electrons, but can also be…

We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we give applications in the studies of the…

Let $k$ be the function field of a complex curve or the field $C((t))$. We show that for a smooth complete intersection $X$ of $r$ hypersurfaces in $P^n_k$ of respective degrees $d_1,...,d_r$ with $\sum d_i^2\leq n+1$ the R-equivalence on…

We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie…

Combinatorial ideas are developed in this article to study Chern numbers on ample and numerically effective vector bundles. An effective lower bound for Chern numbers of ample vector bundles is established, which makes some progress towards…

We consider a Gaussian random matrix theory in the presence of an external matrix source. This matrix model, after duality (a simple version of the closed/open string duality), yields a generalized Kontsevich model through an appropriate…

Intersection graphs of planar geometric objects such as intervals, disks, rectangles and pseudo-disks are well studied. Motivated by various applications, Butman et al. in SODA 2007 considered algorithmic questions in intersection graphs of…

Let M be a U(1) bundle over a smooth Riemann surface. I show that for Chern-Simons theory on M, with structure group G, the path integral is an integral over the space of G-connections on the Riemann surface involving characteristic classes…