Some topological conditions for projective	algebraic manifolds with degenerate	dual varieties: connections with $\mathbf{P}$-bundles

Antonio Lanteri; Daniele Struppa

Displaying similar documents to “Some topological conditions for projective algebraic manifolds with degenerate dual varieties: connections with $\mathbf{P}$ -bundles”

Some topological conditions for projective algebraic manifolds with degenerate dual varieties: connections with $\mathbf{P}$ -bundles

Antonio Lanteri, Daniele Struppa (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si illustrano alcune relazioni tra le varietà proiettive complesse con duale degenere, le varietà la cui topologia si riflette in quella della sezione iperpiana in misura maggiore dell'ordinario e le varietà fibrate in spazi lineari su di una curva.

The finiteness of compact varieties in $C^{n}$

Walter Rudin (1981)

Annales Polonici Mathematici

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Asymptotics of eigensections on toric varieties

A. Huckleberry, H. Sebert (2013)

Annales de l’institut Fourier

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Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities $| ϕ_{n} |^{2} = | s_{N} |^{2} / | | s_{N} {| |}_{L^{2}}^{2}$ for eigensections $s_{N} \in Γ (X, L^{N})$ approaching a semiclassical ray. Here $X$ is a normal compact toric variety and $L$ is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate...

Finiteness of cominuscule quantum $K$ -theory

Anders S. Buch, Pierre-Emmanuel Chaput, Leonardo C. Mihalcea, Nicolas Perrin (2013)

Annales scientifiques de l'École Normale Supérieure

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The product of two Schubert classes in the quantum $K$ -theory ring of a homogeneous space $X = G / P$ is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on $X$ . We show that if $X$ is cominuscule, then this power series has only finitely many non-zero terms. The proof is based on a geometric study of boundary Gromov-Witten varieties in the Kontsevich moduli space, consisting of stable maps to $X$ that take the marked points to general Schubert varieties and...

Categorical equivalences of varieties generated by algebras $𝔄$ and $𝔄^{r}$

K. Denecke (1988)

Banach Center Publications

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Algebraic cobordism of bundles on varieties

Y.-P. Lee, Rahul Pandharipande (2012)

Journal of the European Mathematical Society

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The double point relation defines a natural theory of algebraic cobordism for bundles on varieties. We construct a simple basis (over $ℚ$ ) of the corresponding cobordism groups over Spec( $ℂ$ ) for all dimensions of varieties and ranks of bundles. The basis consists of split bundles over products of projective spaces. Moreover, we prove the full theory for bundles on varieties is an extension of scalars of standard algebraic cobordism.

Lagrangian fibrations on generalized Kummer varieties

Martin G. Gulbrandsen (2007)

Bulletin de la Société Mathématique de France

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We investigate the existence of Lagrangian fibrations on the generalized Kummer varieties of Beauville. For a principally polarized abelian surface $A$ of Picard number one we find the following: The Kummer variety $K^{n} A$ is birationally equivalent to another irreducible symplectic variety admitting a Lagrangian fibration, if and only if $n$ is a perfect square. And this is the case if and only if $K^{n} A$ carries a divisor with vanishing Beauville-Bogomolov square.

On the dimension of secant varieties

Luca Chiantini, Ciro Ciliberto (2010)

Journal of the European Mathematical Society

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In this paper we generalize Zak’s theorems on tangencies and on linear normality as well as Zak’s definition and classification of Severi varieties. In particular we find sharp lower bounds for the dimension of higher secant varieties of a given variety $X$ under suitable regularity assumptions on $X$ , and we classify varieties for which the bound is attained.

A classification theorem on Fano bundles

Roberto Muñoz, Luis E. Solá Conde, Gianluca Occhetta (2014)

Annales de l’institut Fourier

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In this paper we classify rank two Fano bundles $ℰ$ on Fano manifolds satisfying $H^{2} (X, ℤ) ≅ H^{4} (X, ℤ) ≅ ℤ$ . The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization $ℙ (ℰ)$ , that allows us to obtain the cohomological invariants of $X$ and $ℰ$ . As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.

Hyperbolicity and integral points off divisors in subgeneral position in projective algebraic varieties

Do Duc Thai, Nguyen Huu Kien (2015)

Acta Arithmetica

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The purpose of this article is twofold. The first is to find the dimension of the set of integral points off divisors in subgeneral position in a projective algebraic variety $V \subset ℙ_{k ̅}^{m}$ , where k is a number field. As consequences, the results of Ru-Wong (1991), Ru (1993), Noguchi-Winkelmann (2003) and Levin (2008) are recovered. The second is to show the complete hyperbolicity of the complement of divisors in subgeneral position in a projective algebraic variety $V \subset ℙ_{ℂ}^{m} .$

Chern classes of vector bundles with singular connections

Guiseppe De Cecco (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si fa vedere che alcune classi di Chern di fibrati vettoriali complessi possono essere costruite non solo partendo da connessioni $C^{\infty}$ ma, sotto certe condizioni, anche da connessioni lineari singolari. Nel caso particolare del fibrato tangente possono essere costruite anche a partire da metriche singolari. Viene fatto uso in modo essenziale della $L_{2}$ -coomologia di de Rham (introdotta da Cheeger e Teleman).

Interpolating discrete multiplicity varieties for $A ⁰_{p} (ℂ ⁿ)$

Bao Qin Li, Enrique Villamor (2006)

Studia Mathematica

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A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space $A ⁰_{p} (ℂ ⁿ)$ .

Special Grassmann manifolds $V_{3}^{4}$ in the projective space $P_{7}$

Josef Vala (1988)

Časopis pro pěstování matematiky

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Birational positivity in dimension $4$

Behrouz Taji (2014)

Annales de l’institut Fourier

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In this paper we prove that for a nonsingular projective variety of dimension at most 4 and with non-negative Kodaira dimension, the Kodaira dimension of coherent subsheaves of $Ω^{p}$ is bounded from above by the Kodaira dimension of the variety. This implies the finiteness of the fundamental group for such an $X$ provided that $X$ has vanishing Kodaira dimension and non-trivial holomorphic Euler characteristic.

Equivariant K-theory of flag varieties revisited and related results

V. Uma (2013)

Colloquium Mathematicae

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We obtain several several results on the multiplicative structure constants of the T-equivariant Grothendieck ring $K_{T} (G / B)$ of the flag variety G/B. We do this by lifting the classes of the structure sheaves of Schubert varieties in $K_{T} (G / B)$ to R(T) ⊗ R(T), where R(T) denotes the representation ring of the torus T. We further apply our results to describe the multiplicative structure constants of $K {(X)}_{ℚ}$ where X denotes the wonderful compactification of the adjoint group of G, in terms of the structure...

$G$ -тождества и $G$ -многообразия

М.Г. Амаглобели, В.Н. Ремесленников (2000)

Algebra i Logika

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Varieties of Algebras of Polynomial Growth

Daniela La Mattina (2008)

Bollettino dell'Unione Matematica Italiana

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Let $\mathcal{V}$ be a proper variety of associative algebras over a field $F$ of characteristic zero. It is well-known that $\mathcal{V}$ can have polynomial or exponential growth and here we present some classification results of varieties of polynomial growth. In particular we classify all subvarieties of the varieties of almost polynomial growth, i.e., the subvarieties of $\operatorname{\textbf{var}}(G)$ and $\operatorname{\textbf{var}}(UT_{2})$ , where $G$ is the Grassmann algebra and $UT_{2}$ is the algebra of $2\times 2$ upper triangular matrices.

Polarizations of Prym varieties for Weyl groups via abelianization

Herbert Lange, Christian Pauly (2009)

Journal of the European Mathematical Society

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Let $π : Z \to X$ be a Galois covering of smooth projective curves with Galois group the Weyl group of a simple and simply connected Lie group $G$ . For any dominant weight $λ$ consider the curve $Y = Z / Stab (λ)$ . The Kanev correspondence defines an abelian subvariety $P_{λ}$ of the Jacobian of $Y$ . We compute the type of the polarization of the restriction of the canonical principal polarization of $Jac (Y)$ to $P_{λ}$ in some cases. In particular, in the case of the group $E_{8}$ we obtain families of Prym-Tyurin varieties. The main idea is...

On Zariski's theorem in positive characteristic

Ilya Tyomkin (2013)

Journal of the European Mathematical Society

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In the current paper we show that the dimension of a family $V$ of irreducible reduced curves in a given ample linear system on a toric surface $S$ over an algebraically closed field is bounded from above by $- K_{S} . C + p_{g} (C) - 1$ , where $C$ denotes a general curve in the family. This result generalizes a famous theorem of Zariski to the case of positive characteristic. We also explore new phenomena that occur in positive characteristic: We show that the equality $𝚍𝚒𝚖 (V) = - K_{S} . C + p_{g} (C) - 1$ does not imply the nodality of $C$ even if $C$ belongs...

On $2p$ -dimensional Riemannian manifolds with positive scalar curvature

Domenico Perrone (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In questo lavoro si danno alcuni risultati sugli spettri degli operatori di Laplace per varietà Riemanniane compatte con curvatura scalare positiva e di dimensione $2p$ . Ad essi si aggiunge una osservazione riguardante la congettura di Yamabe.

Cyclic actions on $S^{2}$ - and $P^{2}$ -bundles over $S^{1}$

Józef H. Przytycki (1982)

Colloquium Mathematicae

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Chern classes of vector bundles with singular connections

Guiseppe De Cecco (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Displaying similar documents to “Some topological conditions for projective algebraic manifolds with degenerate dual varieties: connections with 𝐏 -bundles”

Displaying similar documents to “Some topological conditions for projective algebraic manifolds with degenerate dual varieties: connections with $\mathbf{P}$ -bundles”