Related papers: Pfaffian Subschemes

The Chern class of the sheaf of logarithmic derivations along a simple normal crossing divisor equals the Chern-Schwartz-MacPherson class of the complement of the divisor. We extend this equality to more general divisors, which are locally…

Let \Sigma be a minimal submanifold of \R^{n+m} that can be represented as the graph of a smooth map f:\R^n-->\R^m. We apply a formula we derived in the study of mean curvature flow to obtain conditions under which \Sigma must be an affine…

Let {\cal T} be a triangulated category, {\cal A} a full subcategory of {\cal T} and {\cal X} a functorially finite subcategory of {\cal A}. If {\cal A} has the properties that any {\cal X}-monomorphism of {\cal A} has a cone and any {\cal…

We show that homeomorphisms $f$ in ${\Bbb R}^n$, $n\geqslant3$, of finite distortion in the Orlicz--Sobolev classes $W^{1,\varphi}_{\rm loc}$ with a condition on $\varphi$ of the Calderon type and, in particular, in the Sobolev classes…

Let V be a smooth equidimensional quasi-affine variety of dimension r over the complex numbers $C$ and let $F$ be a $(p\times s)$-matrix of coordinate functions of $C[V]$, where $s\ge p+r$. The pair $(V,F)$ determines a vector bundle $E$ of…

Let W be a projective variety of dimension n+1, L a free line bundle on W, X in $H^0(L^d)$ a hypersurface of degree d which is generic among those given by sums of monomials from $L$, and let $f : Y \to X$ be a generically finite map from a…

An (association) scheme is said to be Frobenius if it is the scheme of a Frobenius group. A scheme which has the same tensor of intersection numbers as some Frobenius scheme is said to be pseudofrobenius. We establish a necessary and…

The statement of Lemma 3.1 in the published paper is not correct. Lemma 3.1 is needed for the proof of Theorem 3.2. Theorem 3.2 as originally stated is true but its "proof" is not correct. Here we change the statements and proofs of Lemma…

Let $X$ be a Gorenstein minimal projective 3-fold with at worst locally factorial terminal singularities. Suppose the canonical map is of fiber type. Denote by $F$ a smooth model of a generic irreducible component in fibers of the canonical…

Let $X, Y$ be smooth algebraic varieties of the same dimension. Let $f, g : X \to Y$ be finite polynomial mappings. We say that $f, g$ are equivalent if there exists a regular automorphism $\Phi \in Aut(X)$ such that $f = g\circ \Phi$. Of…

It is proved that for any Grothendieck site $X$, there exists a coreflection (called $\mathbf{cosheafification}$) from the category of precosheaves on $X$ with values in a category $\mathbf{K}$, to the full subcategory of cosheaves,…

Given a stratified variety X with strata satisfying a cohomological parity-vanishing condition, we define and show the uniqueness of "parity sheaves", which are objects in the constructible derived category of sheaves with coefficients in…

We show that for $k = 0, 1$ the graph of a continuous mapping $f:D \to \mathbb{R}^k\times\mathbb{C}^p$, defined on a domain $D$ in $\mathbb{C}^n\times\mathbb{R}^k$, is locally foliated by complex $n$-dimensional submanifolds if and only if…

The Grassmannian of affine subspaces is a natural generalization of both the Euclidean space, points being zero-dimensional affine subspaces, and the usual Grassmannian, linear subspaces being special cases of affine subspaces. We show…

For a complex algebraic variety $X$, we show that triviality of the sheaf cohomology group $H^0(X,\mathcal{H}^3)$ occurring on the second page of the Bloch-Ogus spectral sequence follows from a condition on the integral Chow group $CH^2X$…

In this paper, we show that for a given degenerate bivector $\pi= y^n\partial_x \wedge \partial_y$ with $n>1$, the classical Poisson cohomology group and the logarithmic Poisson cohomology group along the ideal…

Let $F$ be a torsionfree semistable coherent sheaf on a polarized normal projective variety. We prove that $F$ has a unique maximal locally free subsheaf $V$ such that $F/V$ is torsionfree and $V$ admits a filtration of subbundles for which…

We study Gorenstein liaison of codimension two subschemes of an arithmetically Gorenstein scheme X. Our main result is a criterion for two such subschemes to be in the same Gorenstein liaison class, in terms of the category of ACM sheaves…

We study the weak Lefschetz property of a class of graded Artinian Gorenstein algebras of codimension three associated in a natural way to the Ap\'ery set of a numerical semigroup generated by four natural numbers. We show that these…

Let $(M^{n},g)$ be a closed, connected, oriented, $C^{\infty}$, Riemannian, n-manifold with a transversely oriented foliation $\boldkey F$. We show that if $\lbrace X,Y \rbrace$ are basic vector fields, the leaf component of $[X,Y]$,…