Related papers: Steiner representations of hypersurfaces

Let X be a smooth hypersurface in projective space. We discuss in this paper when X can be defined by an equation det M = 0 (resp. pf M = 0), where M is a matrix (resp. a skew-symmetric matrix) with homogeneous entries. Standard homological…

If $\mathcal E, \mathcal F$ are vector bundles of ranks $r-1,r$ on a smooth fourfold $X$ and $\mathcal{Hom}(\mathcal E,\mathcal F)$ is globally generated, it is well known that the general map $\phi: \mathcal E \to \mathcal F$ is injective…

Given a nondegenerate ternary form $f=f(x_1,x_2,x_3)$ of degree 4 over an algebraically closed field of characteristic zero, we use the geometry of K3 surfaces and van den Bergh's correspondence between representations of the generalized…

Let X be Drinfeld's upper half space of dimension d over a finite extension K of Q_p. We construct for every homogeneous vector bundle F on the projective space P^d a GL_{d+1}(K)-equivariant filtration by closed K-Frechet spaces on F(X).…

We define a Fourier-Mukai transform for sheaves on K3 surfaces over $\C$, and show that it maps polystable bundles to polystable ones. The role of ``dual'' variety to the given K3 surface $X$ is here played by a suitable component $\hat X$…

Let $X$ be a smooth projective hypersurface of dimension $\geq 5$ and let $E$ be an arithmetically Cohen-Macaulay bundle on $X$ of any rank. We prove that $E$ splits as a direct sum of line bundles if and only if $H^i_*(X, \wedge^2 E) = 0$…

We present results expressing conditions for the existence of meromorphic first integrals for Pfaff equations of arbitrary codimension, integrable or not, on complex manifolds. These results are in the same vein as previous ones by J-P.…

Rank 2 indecomposable arithmetically Cohen-Macaulay bundles E on a nonsingular cubic surface X in P^3 are classified, by means of the possible forms taken by the minimal graded free resolution of E over P^3. The admissible values of the…

We study smooth quadric surfaces in the Pfaffian hypersurface in $\mathbb{P}^{14}$ parameterising $6 \times 6$ skew-symmetric matrices of rank at most 4, not intersecting the Grassmannian $\mathbb{G}(1,5)$. Such surfaces correspond to…

Let X be a K3 surface and M a smooth and projective moduli space of stable sheaves on X of Mukai vector v. A universal sheaf U over X x M induces an integral transform F from the derived category D(X) of coherent sheaves on X to that on M.…

Let $(S,\mathfrak n)$ be a regular local ring and $f$ a non-zero element of $\mathfrak n^2$. A theorem due to Kn\"orrer states that there are finitely many isomorphism classes of maximal Cohen-Macaulay $R=S/(f)$-modules if and only if the…

Let $(\mathcal{E}, \phi)$ be a rank two co-Higgs vector bundles on a K\"ahler compact surface $X$ with $\phi\in H^0(X,End(\mathcal{E})\otimes T_X)$ nilpotent. If $(\mathcal{E}, \phi)$ is semi-stable, then one of the following holds up to…

Considering an integer $d>0$, we show the existence of convex-cocompactrepresentations of surface groups into SO(4,1) admitting an embedded minimal map withcurvatures in $(-1,1)$ and whose associated hyperbolic 4-manifolds are disk bundles…

Given a complex manifold $X$, any K\"ahler class defines an affine bundle over $X$, and any K\"ahler form in the given class defines a totally real embedding of $X$ into this affine bundle. We formulate conditions under which the affine…

We give examples of subcanonical subvarieties of codimension 3 in projective n-space which are not Pfaffian, i.e. defined by the ideal sheaf of submaximal Pfaffians of an alternating map of vector bundles. This gives a negative answer to a…

We study Fell bundles on groupoids from the viewpoint of quantale theory. Given any saturated upper semicontinuous Fell bundle $\pi:E\to G$ on an \'etale groupoid $G$ with $G_0$ locally compact Hausdorff, equipped with a suitable completion…

To fix the bundle moduli of a heterotic compactification one has to understand the Pfaffian one-loop prefactor of the classical instanton contribution. For compactifications on elliptically fibered Calabi-Yau spaces X this can be made…

In this article we extend the notion of determinantal representation of hypersurfaces to the determinantal representation of sections of the determinant line bundle of a vector bundle. We give several examples, and prove some necessary…

Let X be a K3 surface of degree 8 in P^5 with hyperplane section H. We associate to it another K3 surface M which is a double cover of P^2 ramified on a sextic curve C. In the generic case when X is smooth and a complete intersection of…

Given a smooth non-hyperelliptic prime Fano threefold X, we prove the existence of all rank 2 ACM vector bundles on X by deformation of semistable sheaves. We show that these bundles move in generically smooth components of the…