相关论文: Residual intersection theory with reducible scheme…
Consider a collection of vector subspaces of a given vector space and a collection of projectors on these vector spaces, can we decompose the vector space into a product of vector subspaces such that the projectors are isomorphic to…
We define degeneracy loci for vector bundles with structure group $G_2$, and give formulas for their cohomology (or Chow) classes in terms of the Chern classes of the bundles involved. When the base is a point, such formulas are part of the…
In this paper we compare different notions of transversality for possible singular complex algebraic or analytic subsets of an ambient complex manifold and prove a refined intersection formula for their Chern-Schwartz-MacPherson classes. In…
In this note, we present a topological proof of the generalized Lelong-Poincar\'e formula. More precisely, when the zero locus of a section has a pure codimension equal to the rank of a holomorphic vector bundle, the top Chern class of the…
Any arrangement of hyperplanes in general position in $P^n$ can be regarded as a divisor with normal crossing. We study the bundles of logarithmic 1-forms corresponding to such divisors` from the point of view of classification of vector…
Recently it has been shown that the heuristic Rosenfeld functional derives from the virial expansion for particles which overlap in one center. Here, we generalize this approach to any number of intersections. Starting from the virial…
We investigate the globally generated vector bundles on complete intersection Calabi-Yau threefolds with the first Chern class at most 2. We classify all the globally generated vector bundles of an arbitrary rank on quintic in…
In this article we announce some results on compactifying moduli spaces of rank-2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so called bubbling of vector…
The paper is a part of our program to build up a theory of couting immersed nodal curve on algebraic surfaces, as an enumerative Riemann-Roch theory (outlined in math.AG/0405113). In this paper, we discuss the excess intersection theory of…
In this paper, we give a combinatorial formula for the \v{C}ech cocycles representing the power sums of the Chern roots of a holomorphic vector bundle over a complex manifold. By an observation motivation by author's previous paper, we also…
We use hypersurfaces containing unexpected linear spaces to construct interesting vector bundles on complete intersection surfaces in projective space. We discover examples of moduli spaces of rank 2 stable bundles on surfaces of Picard…
By proving an integral formula of the curvature tensor of $E\ts \det E$, we observe that the curvature tensor of $E\ts \det E$ is very similar to that of a line bundle and obtain certain new Kodaira-Akizuki-Nakano type vanishing theorems…
We describe the integral equivariant cohomology ring of a weighted projective space in terms of piecewise polynomials, and thence by generators and relations. We deduce that the ring is a perfect invariant, and prove a Chern class formula…
Let $A$ denote an affine algebra over an algebraically closed field $k$, with $\dim A=d\geq 3$. In the light of availability of cancellation theorems for stably free modules $P$ with $rank(P)=d-1$ (corank one), we try to implement the…
We bound from below the complexity of the top Chern class of the Hodge bundle in the Chow ring of the moduli space of curves: no formulas in terms of classes of degrees 1 and 2 can exist. As a consequence of the Torelli map, the 0-section…
Given a vector bundle $E$ of rank $r$ and degree $d$ on a curve $C$ of genus $g$, one can associate to $E$ in a natural way several other vector bundles. For example, one can take wedge powers of $E$. If $E$ is generated by global sections,…
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 provide formulas for the degrees of the projections of the locus of square matrices with given rank from linear spaces spanned by a choice of matrix entries. The motivation for these computations stem from applications to `matrix…
One describes, using a detailed analysis of Atiyah--Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This…
We present exact computations of partition functions of singlet vector models (infinite level Chern-Simons-matter theories) on lens spaces L(p, 1). We identify light topological configurations and their spectra, and we comment on the…