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Search: All articles in the CMB digital archive with keyword projective

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1. CMB Online first

Zheng, Yuefei; Huang, Zhaoyong
 Triangulated Equivalences Involving Gorenstein Projective Modules For any ring $R$, we show that, in the bounded derived category $D^{b}(\operatorname{Mod} R)$ of left $R$-modules, the subcategory of complexes with finite Gorenstein projective (resp. injective) dimension modulo the subcategory of complexes with finite projective (resp. injective) dimension is equivalent to the stable category $\underline{\mathbf{GP}}(\operatorname{Mod} R)$ (resp. $\overline{\mathbf{GI}}(\operatorname{Mod} R)$) of Gorenstein projective (resp. injective) modules. As a consequence, we get that if $R$ is a left and right noetherian ring admitting a dualizing complex, then $\underline{\mathbf{GP}}(\operatorname{Mod} R)$ and $\overline{\mathbf{GI}}(\operatorname{Mod} R)$ are equivalent. Keywords:triangulated equivalence, Gorenstein projective module, stable category, derived category, homotopy categoryCategories:18G25, 16E35

2. CMB Online first

Takahashi, Tomokuni
 Projective plane bundles over an elliptic curve We calculate the dimension of cohomology groups for the holomorphic tangent bundles of each isomorphism class of the projective plane bundle over an elliptic curve. As an application, we construct the families of projective plane bundles, and prove that the families are effectively parametrized and complete. Keywords:projective plane bundle, vector bundle, elliptic curve, deformation, Kodaira-Spencer mapCategories:14J10, 14J30, 14D15

3. CMB 2017 (vol 60 pp. 235)

Basu, Samik; Subhash, B
 Topology of Certain Quotient Spaces of Stiefel Manifolds We compute the cohomology of the right generalised projective Stiefel manifolds. Following this, we discuss some easy applications of the computations to the ranks of complementary bundles, and bounds on the span and immersibility. Keywords:projective Stiefel manifold, span, spectral sequenceCategories:55R20, 55R25, 57R20

4. CMB 2016 (vol 60 pp. 510)

Haase, Christian; Hofmann, Jan
 Convex-normal (Pairs of) Polytopes In 2012 Gubeladze (Adv. Math. 2012) introduced the notion of $k$-convex-normal polytopes to show that integral polytopes all of whose edges are longer than $4d(d+1)$ have the integer decomposition property. In the first part of this paper we show that for lattice polytopes there is no difference between $k$- and $(k+1)$-convex-normality (for $k\geq 3$) and improve the bound to $2d(d+1)$. In the second part we extend the definition to pairs of polytopes. Given two rational polytopes $P$ and $Q$, where the normal fan of $P$ is a refinement of the normal fan of $Q$. If every edge $e_P$ of $P$ is at least $d$ times as long as the corresponding face (edge or vertex) $e_Q$ of $Q$, then $(P+Q)\cap \mathbb{Z}^d = (P\cap \mathbb{Z}^d ) + (Q \cap \mathbb{Z}^d)$. Keywords:integer decomposition property, integrally closed, projectively normal, lattice polytopesCategories:52B20, 14M25, 90C10

5. CMB 2016 (vol 59 pp. 824)

Karpenko, Nikita A.
 Incompressibility of Products of Pseudo-homogeneous Varieties We show that the conjectural criterion of $p$-incompressibility for products of projective homogeneous varieties in terms of the factors, previously known in a few special cases only, holds in general. Actually, the proof goes through for a wider class of varieties which includes the norm varieties associated to symbols in Galois cohomology of arbitrary degree. Keywords:algebraic groups, projective homogeneous varieties, Chow groups and motives, canonical dimension and incompressibilityCategories:20G15, 14C25

6. CMB 2015 (vol 58 pp. 824)

Luo, Xiu-Hua
 Exact Morphism Category and Gorenstein-projective Representations Let $Q$ be a finite acyclic quiver, $J$ be an ideal of $kQ$ generated by all arrows in $Q$, $A$ be a finite-dimensional $k$-algebra. The category of all finite-dimensional representations of $(Q, J^2)$ over $A$ is denoted by $\operatorname{rep}(Q, J^2, A)$. In this paper, we introduce the category $\operatorname{exa}(Q,J^2,A)$, which is a subcategory of $\operatorname{rep}{}(Q,J^2,A)$ of all exact representations. The main result of this paper explicitly describes the Gorenstein-projective representations in $\operatorname{rep}{}(Q,J^2,A)$, via the exact representations plus an extra condition. As a corollary, $A$ is a self-injective algebra, if and only if the Gorenstein-projective representations are exactly the exact representations of $(Q, J^2)$ over $A$. Keywords:representations of a quiver over an algebra, exact representations, Gorenstein-projective modulesCategory:18G25

7. CMB 2013 (vol 57 pp. 72)

Grari, A.

8. CMB 2011 (vol 56 pp. 306)

Pérez, Juan de Dios; Suh, Young Jin
 Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator is Lie $\mathbb{D}$-parallel We prove the non-existence of real hypersurfaces in complex projective space whose structure Jacobi operator is Lie $\mathbb{D}$-parallel and satisfies a further condition. Keywords:complex projective space, real hypersurface, structure Jacobi operatorCategories:53C15, 53C40

9. CMB 2011 (vol 56 pp. 203)

Tall, Franklin D.
 Productively LindelÃ¶f Spaces May All Be $D$ We give easy proofs that (a) the Continuum Hypothesis implies that if the product of $X$ with every LindelÃ¶f space is LindelÃ¶f, then $X$ is a $D$-space, and (b) Borel's Conjecture implies every Rothberger space is Hurewicz. Keywords:productively LindelÃ¶f, $D$-space, projectively $\sigma$-compact, Menger, HurewiczCategories:54D20, 54B10, 54D55, 54A20, 03F50

10. CMB 2011 (vol 55 pp. 138)

Li, Benling; Shen, Zhongmin
 Projectively Flat Fourth Root Finsler Metrics In this paper, we study locally projectively flat fourth root Finsler metrics and their generalized metrics. We prove that if they are irreducible, then they must be locally Minkowskian. Keywords:projectively flat, Finsler metric, fourth root Finsler metricCategory:53B40

11. CMB 2011 (vol 55 pp. 164)

Pergher, Pedro L. Q.
 Involutions Fixing $F^n \cup \{\text{Indecomposable}\}$ Let $M^m$ be an $m$-dimensional, closed and smooth manifold, equipped with a smooth involution $T\colon M^m \to M^m$ whose fixed point set has the form $F^n \cup F^j$, where $F^n$ and $F^j$ are submanifolds with dimensions $n$ and $j$, $F^j$ is indecomposable and $n >j$. Write $n-j=2^pq$, where $q \ge 1$ is odd and $p \geq 0$, and set $m(n-j) = 2n+p-q+1$ if $p \leq q + 1$ and $m(n-j)= 2n + 2^{p-q}$ if $p \geq q$. In this paper we show that $m \le m(n-j) + 2j+1$. Further, we show that this bound is \emph{almost} best possible, by exhibiting examples $(M^{m(n-j) +2j},T)$ where the fixed point set of $T$ has the form $F^n \cup F^j$ described above, for every $2 \le j Keywords:involution, projective space bundle, indecomposable manifold, splitting principle, Stiefel-Whitney class, characteristic numberCategory:57R85 12. CMB 2011 (vol 54 pp. 422) Pérez, Juan de Dios; Suh, Young Jin  Two Conditions on the Structure Jacobi Operator for Real Hypersurfaces in Complex Projective Space We classify real hypersurfaces in complex projective space whose structure Jacobi operator satisfies two conditions at the same time. Keywords:complex projective space, real hypersurface, structure Jacobi operator, two conditionsCategories:53C15, 53B25 13. CMB 2009 (vol 52 pp. 84) Gauthier, P. M.; Zeron, E. S.  Hartogs' Theorem on Separate Holomorphicity for Projective Spaces If a mapping of several complex variables into projective space is holomorphic in each pair of variables, then it is globally holomorphic. Keywords:separately holomorphic, projective spaceCategories:32A10, 32D99, 32H99 14. CMB 2002 (vol 45 pp. 349) Coppens, Marc  Very Ample Linear Systems on Blowings-Up at General Points of Projective Spaces Let$\mathbf{P}^n$be the$n$-dimensional projective space over some algebraically closed field$k$of characteristic$0$. For an integer$t\geq 3$consider the invertible sheaf$O(t)$on$\mathbf{P}^n$(Serre twist of the structure sheaf). Let$N = \binom{t+n}{n}$, the dimension of the space of global sections of$O(t)$, and let$k$be an integer satisfying$0\leq k\leq N - (2n+2)$. Let$P_1,\dots,P_k$be general points on$\mathbf{P}^n$and let$\pi \colon X \to \mathbf{P}^n$be the blowing-up of$\mathbf{P}^n$at those points. Let$E_i = \pi^{-1} (P_i)$with$1\leq i\leq k$be the exceptional divisor. Then$M = \pi^* \bigl( O(t) \bigr) \otimes O_X (-E_1 - \cdots -E_k)$is a very ample invertible sheaf on$X\$. Keywords:blowing-up, projective space, very ample linear system, embeddings, Veronese mapCategories:14E25, 14N05, 14N15
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