Pieri-type intersection formulas and primary obstructions for decomposing 2-forms

Sinan Sertöz

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Displaying similar documents to “Pieri-type intersection formulas and primary obstructions for decomposing 2-forms”

Inverse eigenvalue problem of cell matrices

Sreyaun Khim, Kijti Rodtes (2019)

Czechoslovak Mathematical Journal

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We consider the problem of reconstructing an $n \times n$ cell matrix $D (\vec{x})$ constructed from a vector $\vec{x} = (x_{1}, x_{2}, \dots, x_{n})$ of positive real numbers, from a given set of spectral data. In addition, we show that the spectra of cell matrices $D (\vec{x})$ and $D (π (\vec{x}))$ are the same for every permutation $π \in S_{n}$ .

Chern rank of complex bundle

Bikram Banerjee (2019)

Commentationes Mathematicae Universitatis Carolinae

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Motivated by the work of A. C. Naolekar and A. S. Thakur (2014) we introduce notions of upper chern rank and even cup length of a finite connected CW-complex and prove that upper chern rank is a homotopy invariant. It turns out that determination of upper chern rank of a space $X$ sometimes helps to detect whether a generator of the top cohomology group can be realized as Euler class for some real (orientable) vector bundle over $X$ or not. For a closed connected $d$ -dimensional complex manifold...

Representations of a class of positively based algebras

Shiyu Lin, Shilin Yang (2023)

Czechoslovak Mathematical Journal

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We investigate the representation theory of the positively based algebra $A_{m, d}$ , which is a generalization of the noncommutative Green algebra of weak Hopf algebra corresponding to the generalized Taft algebra. It turns out that $A_{m, d}$ is of finite representative type if $d \leq 4$ , of tame type if $d = 5$ , and of wild type if $d \geq 6 .$ In the case when $d \leq 4$ , all indecomposable representations of $A_{m, d}$ are constructed. Furthermore, their right cell representations as well as left cell representations of $A_{m, d}$ are described. ...

Liftings of 1-forms to $(J^{r} T ) $

Włodzimierz M. Mikulski (2002)

Colloquium Mathematicae

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Let $J^{r} T * M$ be the r-jet prolongation of the cotangent bundle of an n-dimensional manifold M and let $(J^{r} T * M) *$ be the dual vector bundle. For natural numbers r and n, a complete classification of all linear natural operators lifting 1-forms from M to 1-forms on $(J^{r} T * M) *$ is given.

Global classical solutions in a self-consistent chemotaxis(-Navier)-Stokes system

Yanjiang Li, Zhongqing Yu, Yumei Huang (2024)

Czechoslovak Mathematical Journal

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The self-consistent chemotaxis-fluid system $\{\begin{matrix} n_{t} + u \cdot \nabla n = Δ n - \nabla \cdot (n \nabla c) + \nabla \cdot (n \nabla φ), & x \in Ω, t > 0, \\ c_{t} + u \cdot \nabla c = Δ c - n c, & x \in Ω, t > 0, \\ u_{t} + κ (u \cdot \nabla) u + \nabla P = Δ u - n \nabla φ + n \nabla c, & x \in Ω, t > 0, \\ \nabla \cdot u = 0, & x \in Ω, t > 0, \end{matrix}$ is considered under no-flux boundary conditions for $n, c$ and the Dirichlet boundary condition for $u$ on a bounded smooth domain $Ω \subset ℝ^{N}$ $(N = 2, 3)$ , $κ \in {0, 1}$ . The existence of global bounded classical solutions is proved under a smallness assumption on $∥ c_{0} ∥_{L^{\infty} (Ω)}$ . Both the effect of gravity (potential force) on cells and the effect of the chemotactic force on fluid are considered here, and thus the coupling is stronger than the most studied chemotaxis-fluid...

On natural vector bundle morphisms $T_{A} \circ ⨂_{s}^{q} \to ⨂_{s}^{q} \circ T_{A}$ over $i d_{T_{A}}$

A. Ntyam, A. Mba (2009)

Annales Polonici Mathematici

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Some properties and applications of natural vector bundle morphisms $T_{A} \circ ⨂_{s}^{q} \to ⨂_{s}^{q} \circ T_{A}$ over $i d_{T_{A}}$ are presented.

Bounds for the characteristic rank and cup-length of oriented Grassmann manifolds

Tomáš Rusin (2018)

Archivum Mathematicum

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We estimate the characteristic rank of the canonical $k$ –plane bundle over the oriented Grassmann manifold ${\tilde{G}}_{n, k}$ . We then use it to compute uniform upper bounds for the $ℤ_{2}$ –cup-length of ${\tilde{G}}_{n, k}$ for $n$ belonging to certain intervals.

Geometric stability of the cotangent bundle and the universal cover of a projective manifold

Frédéric Campana, Thomas Peternell (2011)

Bulletin de la Société Mathématique de France

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We first prove a strengthening of Miyaoka’s generic semi-positivity theorem: the quotients of the tensor powers of the cotangent bundle of a non-uniruled complex projective manifold $X$ have a pseudo-effective (instead of generically nef) determinant. A first consequence is that $X$ is of general type if its cotangent bundle contains a subsheaf with ‘big’ determinant. Among other applications, we deduce that if the universal cover of $X$ is not covered by compact positive-dimensional analytic...

On the connectivity of finite subset spaces

Jacob Mostovoy, Rustam Sadykov (2012)

Fundamenta Mathematicae

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We prove that the space $e x p_{k} ⋁ S^{m + 1}$ of nonempty subsets of cardinality at most k in a bouquet of m+1-dimensional spheres is (m+k-2)-connected. This, as shown by Tuffley, implies that the space $e x p_{k} X$ is (m+k-2)-connected for any m-connected cell complex X.

The generic dimension of the first derived system

Robert P. Buemi (1978)

Annales de l'institut Fourier

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Any $r$ -dimensional subbundle of the cotangent bundle on an $n$ -dimensional manifold $M$ partitions $M$ into subsets $M_{0}, ..., M_{m}$ ( $m$ being the minimum of $r$ and $C (n - r, 2)$ , the combinations of $n - r$ things taken 2 at a time). $M_{i}$ is the set on which the first derived systems of the subbundle has codimension $i$ . In this paper we prove the following: Theorem. Let $s \geq 2$ and let $Q$ be a generic $C^{s}$ $r$ -dimensional subbundle of the cotangent bundle of an $n$ -dimensional manifold $M$ . The codimension...

The natural operators lifting 1-forms to some vector bundle functors

J. Kurek, W. M. Mikulski (2002)

Colloquium Mathematicae

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Let F:ℳ f→ ℬ be a vector bundle functor. First we classify all natural operators $T_{| ℳ f ₙ} ⇝ T^{(0, 0)} (F_{| ℳ f ₙ}) *$ transforming vector fields to functions on the dual bundle functor $(F_{| ℳ f ₙ}) *$ . Next, we study the natural operators $T *_{| ℳ f ₙ} ⇝ T * (F_{| ℳ f ₙ}) *$ lifting 1-forms to $(F_{| ℳ f ₙ}) *$ . As an application we classify the natural operators $T *_{| ℳ f ₙ} ⇝ T * (F_{| ℳ f ₙ}) *$ for some well known vector bundle functors F.

Constructions on second order connections

J. Kurek, W. M. Mikulski (2007)

Annales Polonici Mathematici

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We classify all $ℱ ℳ_{m, n}$ -natural operators $: J ² ⟿ J ² V^{A}$ transforming second order connections Γ: Y → J²Y on a fibred manifold Y → M into second order connections $(Γ) : V^{A} Y \to J ² V^{A} Y$ on the vertical Weil bundle $V^{A} Y \to M$ corresponding to a Weil algebra A.

Natural operators lifting linear vector fields from a vector bundle to its r-jet prolongations

Włodzimierz M. Mikulski (2003)

Annales Polonici Mathematici

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All natural operators A transforming a linear vector field X on a vector bundle E into a vector field A(X) on the r-jet prolongation $J^{r} E$ of E are given. Similar results are deduced for the r-jet prolongations $J_{v}^{r} E$ and $J^{[r]} E$ in place of $J^{r} E$ .

Existence problem of the osculating planes of a curve in $R_{n}$

S. Topa (1964)

Annales Polonici Mathematici

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Special modules for $R (PSL (2, q))$

Liufeng Cao, Huixiang Chen (2023)

Czechoslovak Mathematical Journal

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Let $R$ be a fusion ring and $R_{ℂ} : = R \otimes_{ℤ} ℂ$ be the corresponding fusion algebra. We first show that the algebra $R_{ℂ}$ has only one left (right, two-sided) cell and the corresponding left (right, two-sided) cell module. Then we prove that, up to isomorphism, $R_{ℂ}$ admits a unique special module, which is 1-dimensional and given by the Frobenius-Perron homomorphism FPdim. Moreover, as an example, we explicitly determine the special module of the interpolated fusion algebra $R (PSL (2, q)) : = r (PSL (2, q)) \otimes_{ℤ} ℂ$ up to isomorphism, where $r (PSL (2, q))$ is the...

Lifting to the r-frame bundle by means of connections

J. Kurek, W. M. Mikulski (2010)

Annales Polonici Mathematici

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Let m and r be natural numbers and let $P^{r} : ℳ f_{m} \to ℱ ℳ$ be the rth order frame bundle functor. Let $F : ℳ f_{m} \to ℱ ℳ$ and $G : ℳ f_{k} \to ℱ ℳ$ be natural bundles, where $k = d i m (P^{r} ℝ^{m})$ . We describe all $ℳ f_{m}$ -natural operators A transforming sections σ of $F M \to M$ and classical linear connections ∇ on M into sections A(σ,∇) of $G (P^{r} M) \to P^{r} M$ . We apply this general classification result to many important natural bundles F and G and obtain many particular classifications.

The natural operators lifting horizontal 1-forms to some vector bundle functors on fibered manifolds

J. Kurek, W. M. Mikulski (2003)

Colloquium Mathematicae

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Let F:ℱ ℳ → ℬ be a vector bundle functor. First we classify all natural operators $T_{p r o j | ℱ ℳ_{m, n}} ⇝ T^{(0, 0)} (F_{| ℱ ℳ_{m, n}}) *$ transforming projectable vector fields on Y to functions on the dual bundle (FY)* for any $ℱ ℳ_{m, n}$ -object Y. Next, under some assumption on F we study natural operators $T *_{h o r | ℱ ℳ_{m, n}} ⇝ T * (F_{| ℱ ℳ_{m, n}}) *$ lifting horizontal 1-forms on Y to 1-forms on (FY)* for any Y as above. As an application we classify natural operators $T *_{h o r | ℱ ℳ_{m, n}} ⇝ T * (F_{| ℱ ℳ_{m, n}}) *$ for some vector bundle functors F on fibered manifolds.

The gradient flow of Higgs pairs

Jiayu Li, Xi Zhang (2011)

Journal of the European Mathematical Society

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We consider the gradient flow of the Yang–Mills–Higgs functional of Higgs pairs on a Hermitian vector bundle $(E, H_{0})$ over a Kähler surface $(M, ω)$ , and study the asymptotic behavior of the heat flow for Higgs pairs at infinity. The main result is that the gradient flow with initial condition $(A_{0}, φ_{0})$ converges, in an appropriate sense which takes into account bubbling phenomena, to a critical point $(A_{\infty}, φ_{\infty})$ of this functional. We also prove that the limiting Higgs pair $(A_{\infty}, φ_{\infty})$ can be extended smoothly to a vector bundle...

Zero-set property of o-minimal indefinitely Peano differentiable functions

Andreas Fischer (2008)

Annales Polonici Mathematici

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Given an o-minimal expansion ℳ of a real closed field R which is not polynomially bounded. Let $^{\infty}$ denote the definable indefinitely Peano differentiable functions. If we further assume that ℳ admits $^{\infty}$ cell decomposition, each definable closed subset A of Rⁿ is the zero-set of a $^{\infty}$ function f:Rⁿ → R. This implies $^{\infty}$ approximation of definable continuous functions and gluing of $^{\infty}$ functions defined on closed definable sets.

General position properties in fiberwise geometric topology

Taras Banakh, Vesko Valov

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General position properties play a crucial role in geometric and infinite-dimensional topologies. Often such properties provide convenient tools for establishing various universality results. One of well-known general position properties is DDⁿ, the property of disjoint n-cells. Each Polish $L C^{n - 1}$ -space X possessing DDⁿ contains a topological copy of each n-dimensional compact metric space. This fact implies, in particular, the classical Lefschetz-Menger-Nöbeling-Pontryagin-Tolstova embedding...

Semistability of Frobenius direct images over curves

Vikram B. Mehta, Christian Pauly (2007)

Bulletin de la Société Mathématique de France

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Let $X$ be a smooth projective curve of genus $g \geq 2$ defined over an algebraically closed field $k$ of characteristic $p > 0$ . Given a semistable vector bundle $E$ over $X$ , we show that its direct image $F_{*} E$ under the Frobenius map $F$ of $X$ is again semistable. We deduce a numerical characterization of the stable rank- $p$ vector bundles $F_{*} L$ , where $L$ is a line bundle over $X$ .

Horizontal sections of connections on curves and transcendence

C. Gasbarri (2013)

Acta Arithmetica

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Let K be a number field, X be a smooth projective curve over it and D be a reduced divisor on X. Let (E,∇) be a vector bundle with connection having meromorphic singularities on D. Let $p_{1}, . . ., p_{s} \in X (K)$ and $X^{o} : = X ̅ ∖ D, p_{1}, . . ., p_{s}$ (the $p_{j}$ ’s may be in the support of D). Using tools from Nevanlinna theory and formal geometry, we give the definition of E-section of arithmetic type of the vector bundle E with respect to the points $p_{j}$ ; this is the natural generalization of the notion of E-function defined in Siegel-Shidlovskiĭ...