Algebraic cobordism of bundles on varieties

Y.-P. Lee; Rahul Pandharipande

Displaying similar documents to “Algebraic cobordism of bundles on varieties”

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 Lincei. Matematica e Applicazioni

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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.

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

Walter Rudin (1981)

Annales Polonici Mathematici

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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.

Singular Bundles with Bounded $L^{2}$ -Curvatures

Thiemo Kessel, Tristan Rivière (2008)

Bollettino dell'Unione Matematica Italiana

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We consider calculus of variations of the Yang-Mills functional in dimensions larger than the critical dimension 4. We explain how this naturally leads to a class of - a priori not well-defined - singular bundles including possibly "almost everywhere singular bundles". In order to overcome this difficulty, we suggest a suitable new framework, namely the notion of singular bundles with bounded $L^{2}$ -curvatures.

Equivariant vector bundles on toric varieties and some problems of linear algebra

A. A. Klyachko (1990)

Banach Center Publications

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C-semigroup bundles and C-algebras whose irreducible representations are all finite dimensional

Thomas Müller

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We investigate the structure of C*-algebras with a finite bound on the dimensions of their irreducible representations, sometimes called “subhomogeneous”.In the first chapter we develop the theory of C*-semigroup bundles. These are C*-bundles over semigroups together with a “structure map” which links the semigroup structure of the base space lo the bundle. Under suitable conditions we prove the existence of “enough” bounded sections, which arc “compatible” with the C*-semigroup bundle...

Cohomology of torus bundles over Kuga fiber varieties.

Lee, Min Ho (2008)

Beiträge zur Algebra und Geometrie

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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.

Proof of Nadel’s conjecture and direct image for relative $K$ -theory

Alain Berthomieu (2002)

Bulletin de la Société Mathématique de France

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A “relative” $K$ -theory group for holomorphic or algebraic vector bundles on a compact or quasiprojective complex manifold is constructed, and Chern-Simons type characteristic classes are defined on this group in the spirit of Nadel. In the projective case, their coincidence with the Abel-Jacobi image of the Chern classes of the bundles is proved. Some applications to families of holomorphic bundles are given and two Riemann-Roch type theorems are proved for these classes.

On the motives of moduli of chains and Higgs bundles

Oscar García-Prada, Jochen Heinloth, Alexander Schmitt (2014)

Journal of the European Mathematical Society

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We take another approach to Hitchin’s strategy of computing the cohomology of moduli spaces of Higgs bundles by localization with respect to the circle action. Our computation is done in the dimensional completion of the Grothendieck ring of varieties and starts by describing the classes of moduli stacks of chains rather than their coarse moduli spaces. As an application we show that the $n$ -torsion of the Jacobian acts trivially on the middle dimensional cohomology of the moduli space...

Line bundles with partially vanishing cohomology

Burt Totaro (2013)

Journal of the European Mathematical Society

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Define a line bundle $L$ on a projective variety to be $q$ -ample, for a natural number $q$ , if tensoring with high powers of $L$ kills coherent sheaf cohomology above dimension $q$ . Thus 0-ampleness is the usual notion of ampleness. We show that $q$ -ampleness of a line bundle on a projective variety in characteristic zero is equivalent to the vanishing of an explicit finite list of cohomology groups. It follows that $q$ -ampleness is a Zariski open condition, which is not clear from the definition. ...

Natural operators lifting functions to affinors on higher order cotangent bundles

W. M. Mikulski (2004)

Annales Polonici Mathematici

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For natural numbers n ≥ 3 and r ≥ 1 all natural operators $A : T_{| ℳ f ₙ}^{(0, 0)} ⟿ T^{(1, 1)} T^{r *}$ transforming functions from n-manifolds into affinors (i.e. tensor fields of type (1,1)) on the r-cotangent bundle are classified.

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...

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...

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

Józef H. Przytycki (1982)

Colloquium Mathematicae

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Liftings of functions and vector fields to natural bundles

Jacek Gancarzewicz

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CONTENTS0. Introduction...................................................................................................51. Natural bundles...........................................................................................102. Liftings of functions.....................................................................................153. Liftings of functions to the r-frame bundle...................................................224. A space of liftings of functions.....................................................................265....

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...

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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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).

Actions of $Z_{n}$ on some surface-bundles over $S^{1}$

Józef H. Przytycki (1982)

Colloquium Mathematicae

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$G$ -тождества и $G$ -многообразия

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

Algebra i Logika

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

K. Denecke (1988)

Banach Center Publications

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Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles

Vadim V. Shurygin, Svetlana K. Zubkova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The second order transverse bundle $T_{}^{2} M$ of a foliated manifold $M$ carries a natural structure of a smooth manifold over the algebra $𝔻^{2}$ of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general $𝔻^{2}$ -smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a $𝔻^{2}$ -smooth foliated diffeomorphism between two second order transverse...

Произведения и векторные расслоения в категории $G$ -супермногообразий

К. Барточчи, У. Брудзо, Д.Эрнандес Руйперес (1993)

Sibirskij matematiceskij zurnal

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