Vincenzo Ancona

Bio: Vincenzo Ancona is an academic researcher from University of Florence. The author has contributed to research in topics: Differential form & De Rham cohomology. The author has an hindex of 9, co-authored 27 publications receiving 310 citations.

Complex Analysis and Geometry

Abstract: On the Limits of Manifolds with nef Canonical Bundles, M. Andreatta and T. Peternell On the Stability of the Restriction of TPn to Projective Curves, E. Ballico and B. Russo Theorie des (a,b)-Modules II. Extensions, D. Barlet Moduli of Reflexive K3 Surfaces, C. Bartocci, U. Bruzzo, and D. Hernandez Ruiperez New Examples of Domains with Non-Injective Proper Holomorphic Self-Maps, F. Berteloot and J. J. Loeb Q-Convexivity. A Survey, M. Coltoiu Commuting maps and Families of Hyperbolic Automorphisms, C. de Fabritiis An Alternative Proof of a Theorem of Boas-Straube-Yu, K. Diederich and G. Herbort Large Polynomial Hulls with No Analytic Structure, J. Duval and N. Levenberg Canonical Connections for Almost-Hypercomplex Structures, P. Gauduchon The Tangent Bundle of P2 Restricted to Plane Curves, G. Hein Quotients with Respects to Holomorphic Actions of Reductive Groups, P. Heinzner and L. Migliorini Adjunction Theory on Terminal Varieties, M. Mella Runge Theorem in Higher Dimensions, V. Vajaitu Only Countably Many Simply-Connected Lie Groups Admit Lattices, J. Winkelmann

Some Applications of Beilinson's Theorem to Projective Spaces and Quadrics

Abstract: In this paper we apply the Beilinson theorem [Functional Anal. Appl. 12 (1978), 214-216] to the following problems. (1) We give sufficient cohomological conditions in order that a coherent sheaf on IP or on the quadric contains äs direct summand a generator of the derived category (i. e. the line bundles, the bundles ofp-forms on P\", the spinor bundles and the bundles \\pt introduced by Kapranov [Inv. Math. 92 (1988), 479-508]. (2) We characterize the indecomposable sheaves of order one (with respect to H and H)onP and we show that also the diameter is one. (3) We give a new proof of the key theorem which Chang uses to characterize the arithmetically Buchsbaum subschemes of codimension 2 in P\". 1980 Mathematics Subject Classification (1985 Revision): 14F05.

Unstable hyperplanes for Steiner bundles and multidimensional matrices

Abstract: We study some properties of the natural action of SLOV0U SLOVpU on non- degenerate multidimensional complex matrices A A POV0 n n VpU of boundary format (in the sense of Gelfand, Kapranov and Zelevinsky); in particular we characterize the non-stable ones as the matrices which are in the orbit of a ''triangular'' matrix, and the matrices with a stabilizer containing C as those which are in the orbit of a ''diagonal'' matrix. For pa 2i t turns out that a non-degenerate matrix A A POV0 n V1 n V2U detects a Steiner bundle SA (in the sense of Dolgachev and Kapranov) on the projective space P n , na dimOV2Uˇ1. As a consequence we prove that the symmetry group of a Steiner bundle is contained in SLO2U and that the SLO2U-invariant Steiner bundles are exactly the bundles introduced by Schwarzen- berger (Schw), which correspond to ''identity'' matrices. We can characterize the points of the moduli space of Steiner bundles which are stable for the action of AutOP n U, answering in the first nontrivial case a question posed by Simpson. In the opposite direction we obtain some results about Steiner bundles which imply properties of matrices. For example the number of unstable hyperplanes of SA (counting multiplicities) produces an interesting discrete invariant of A, which can take the values 0; 1; 2; .. .; dim V0a 1o ry; the y case occurs if and only if SA is Schwarzenberger (and A is an identity). Finally, the Gale transform for Steiner bun- dles introduced by Dolgachev and Kapranov under the classical name of association can be understood in this setting as the transposition operator on multidimensional matrices.

Stability of Special Instanton Bundles on ℙ 2n + 1

Abstract: We prove that the special instanton bundles of rank 2n on p2n+ 1 (C) with a symplectic structure studied by Spindler and Trautmann are stable in the sense of Mumford-Takemoto. This implies that the generic special instanton bundle is stable. Moreover all instanton bundles on P5 are stable. We get also the stability of other related vector bundles.

Mixed Hodge Structures

Abstract: With a basic knowledge of cohomology theory, the background necessary to understand Hodge theory and polarization, Deligne's Mixed Hodge Structure on cohomology of complex algebraic varieties is described.

Sheaf Cohomology and Free Resolutions over Exterior Algebras

Abstract: In this paper we derive an explicit version of the Bernstein- Gel'fand-Gel'fand (BGG) correspondence between bounded complexes of coherent sheaves on projective space and minimal doubly infinite free reso- lutions over its "Koszul dual" exterior algebra. Among the facts about the BGG correspondence that we derive is that taking homology of a complex of sheaves corresponds to taking the "linear part" of a resolution over the exterior algebra. We explore the structure of free resolutions over an exterior algebra. For example, we show that such resolutions are eventually dominated by their "linear parts" in the sense that erasing all terms of degree > 1 in the complex yields a new complex which is eventually exact. As applications we give a construction of the Beilinson monad which expresses a sheaf on projective space in terms of its cohomology by using sheaves of differential forms. The explicitness of our version allows us to to prove two conjectures about the morphisms in the monad and we get an efficient method for machine computation of the cohomology ofsheaves. We also construct all the monads for a sheaf that can be built from sums of line bundles, and show that they are often characterized by numerical data. Let V be a finite dimensional vector space over a field K, and let W = V ∗ be the dual space. In this paper we will study complexes and resolutions over the exterior algebra E = ∧V and their relation to modules over S = Sym W and sheaves on projective space P(W). In this paper we study the Bernstein-Gel'fand-Gel'fand (BGG) correspondence (1978), usually stated as an equivalence between the derived category of bounded complexes of coherent sheaves on P(W) and the stable category of finitely generated graded modules over E. Its essential content is a functor R from complexes of graded S-modules to complexes of graded E-modules, and its adjoint L. For example, if M = ⊕iMi is a graded S-module (regarded as a complex with just one term) then ∗ The first and third authors are grateful to the NSF for partial support during the preparation of this paper. The third author wishes to thank MSRI for its hospitality.

Suita conjecture and the Ohsawa-Takegoshi extension theorem

Abstract: We prove a conjecture of N. Suita which says that for any bounded domain D in ℂ one has $c_{D}^{2}\leq\pi K_{D}$ , where c D (z) is the logarithmic capacity of ℂ∖D with respect to z∈D and K D the Bergman kernel on the diagonal. We also obtain optimal constant in the Ohsawa-Takegoshi extension theorem.

Regularization of closed positive currents of type (1,1) by the flow of a Chern connection

Abstract: Let X be a compact n-dimensional complex manifold and let T be a closed positive current of bidegree (1, 1) on X. In general, T cannot be approximated by closed positive currents of class C ∞: a necessary condition for this is that the cohomology class {T} is numerically effective in the sense that ∫ Y {T} P ≥ 0 for every p-dimensional subvariety Y ⊂ X. For example, if E ≃ ℙ n−1 is the exceptional divisor of a one-point blow-up X → X′, then T = [E] cannot be positively approximated: for every curve C ⊂ E, we have ∫ C {E} = ∫ C c 1(O(−1)) < 0. However, we will see that it is always possible to approximate a closed positive current T of type (1, 1) by closed real currents admitting a small negative part, and that this negative part can be estimated in terms of the Lelong numbers of T and the geometry of X.