Related papers: Chern Classes of Logarithmic Vector Fields

Baker and Norine proved a Riemann--Roch theorem for divisors on undirected graphs. The notions of graph divisor theory are in duality with the notions of the chip-firing game of Bj\"orner, Lov\'asz and Shor. We use this connection to prove…

We derive an explicit formula for the well-known Chern-Moser-Weyl tensor for nondegenerate real hypersurfaces in complex space in terms of their defining functions. The formula is considerably simplified when applying to "pluriharmonic…

Every polynomial of the form $P=(x+1)(x^{n-1}+c_1x^{n-2}+\cdots +c_{n-1})$ is representable as Schur-Szeg\H{o} composition of $n-1$ polynomials of the form $(x+1)^{n-1}(x+a_i)$, where the numbers $a_i$ are unique up to permutation. We give…

Khimshiashvili proved a topological degree formula for the Eu-ler characteristic of the Milnor fibres of a real function-germ with an isolated singularity. We give two generalizations of this result for non-isolated singularities. As…

In [1] M. Baker and S. Norine developed a theory of divisors and linear systems on graphs, and proved a Riemann-Roch Theorem for these objects (conceived as integer-valued functions on the vertices). In [2] and [3] the authors generalized…

Let S be a generic C-infinity smooth CR manifold in C^n, n > 1, and let M be a generic C-infinity CR submanifold of S X C^m. We prescribe conditions on M so that it is the disjoint union of graphs of CR maps f:S-->C^m. We also consider the…

We consider in this paper an area functional defined on submanifolds of fixed degree immersed into a graded manifold equipped with a Riemannian metric. Since the expression of this area depends on the degree, not all variations are…

Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: 1. X is in the C1-interior of the set of expansive divergence-free vector…

We prove that every closed set which is not sigma-finite with respect to the Hausdorff measure H^{N-1} carries singularities of continuous vector fields in the Euclidean space R^N for the divergence operator. We also show that finite…

We prove that if $X---> X^+$ is a threefold terminal flip, then $c_1(X).c_2(X)\leq c_1(X^+).c_2(X^+)$ where $c_1(X)$ and $c_2(X)$ denote the Chern classes. This gives the affirmative answer to a Question by Xie \cite{Xie2}. We obtain the…

In this paper, we study the homogeneous components of the Chern--Schwartz--MacPherson (CSM) classes of Schubert cells. We prove that, under suitable conditions, each such component is represented by an irreducible subvariety. In particular,…

We study the algebraic rank of a divisor on a graph, an invariant defined using divisors on algebraic curves dual to the graph. We prove it satisfies the Riemann-Roch formula, a specialization property, and the Clifford inequality. We prove…

In this paper, we prove that the conductor formula of Bloch implies the conjecture of Deligne on Milnor numbers of isolated singularities. In particular, thanks to the work of Bloch on his conjecture, our result implies that this so-called…

In this paper a formula is proved for the general degeneracy locus associated to an oriented quiver of type A_n. Given a finite sequence of vector bundles with maps between them, these loci are described by putting rank conditions on…

We prove that for any number $r$ in $[2,3]$, there are spin (resp. non-spin minimal) simply connected complex surfaces of general type $X$ with $c_1^2(X)/c_2(X)$ arbitrarily close to $r$. In particular, this shows the existence of simply…

In the theory of algebraic function fields and their applications to the information theory, the Riemann-Roch theorem plays a fundamental role. But its use, delicate in general, is efficient and practical for applications especially in the…

We show that assuming the generalized Riemann hypothesis there are no normal CM-fields with class number one of degree 64 and 96. This is done by constructing complete tables of normal CM-fields using discriminant bounds of Lee--Kwon. This…

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…

Let C be a projective curve defined over a field k and let D be a divisor of C. The Riemann-Roch space L(D) is the set of rational functions on C for which certain zeros are imposed and certain poles are allowed, with some multiplicities…

Since the works of Krasnov and Scheiderer, there has been an interest in studying effective totally real divisors on a curve X defined over a real closed field, i.e., effective divisors supported on the real locus. Scheiderer proved that,…