Displaying similar documents to “A note on the cohomology ring of the oriented Grassmann manifolds G ˜ n , 4

1 -cocycles on the group of contactomorphisms on the supercircle S 1 | 3 generalizing the Schwarzian derivative

Boujemaa Agrebaoui, Raja Hattab (2016)

Czechoslovak Mathematical Journal

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The relative cohomology H diff 1 ( 𝕂 ( 1 | 3 ) , 𝔬𝔰𝔭 ( 2 , 3 ) ; 𝒟 λ , μ ( S 1 | 3 ) ) of the contact Lie superalgebra 𝕂 ( 1 | 3 ) with coefficients in the space of differential operators 𝒟 λ , μ ( S 1 | 3 ) acting on tensor densities on S 1 | 3 , is calculated in N. Ben Fraj, I. Laraied, S. Omri (2013) and the generating 1 -cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative 1 -cocycle s ( X f ) = D 1 D 2 D 3 ( f ) α 3 1 / 2 , X f 𝕂 ( 1 | 3 ) which is invariant with respect to the conformal subsuperalgebra 𝔬𝔰𝔭 ( 2 , 3 ) of 𝕂 ( 1 | 3 ) . In this work we study the supergroup case. We give an explicit construction of 1 -cocycles...

Invariants, torsion indices and oriented cohomology of complete flags

Baptiste Calmès, Viktor Petrov, Kirill Zainoulline (2013)

Annales scientifiques de l'École Normale Supérieure

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Let  G be a split semisimple linear algebraic group over a field and let  T be a split maximal torus of  G . Let  𝗁 be an oriented cohomology (algebraic cobordism, connective K -theory, Chow groups, Grothendieck’s K 0 , etc.) with formal group law F . We construct a ring from F and the characters of  T , that we call a formal group ring, and we define a characteristic ring morphism c from this formal group ring to  𝗁 ( G / B ) where G / B is the variety of Borel subgroups of  G . Our main result says that when the...

S -depth on Z D -modules and local cohomology

Morteza Lotfi Parsa (2021)

Czechoslovak Mathematical Journal

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Let R be a Noetherian ring, and I and J be two ideals of R . Let S be a Serre subcategory of the category of R -modules satisfying the condition C I and M be a Z D -module. As a generalization of the S - depth ( I , M ) and depth ( I , J , M ) , the S - depth of ( I , J ) on M is defined as S - depth ( I , J , M ) = inf { S - depth ( 𝔞 , M ) : 𝔞 W ˜ ( I , J ) } , and some properties of this concept are investigated. The relations between S - depth ( I , J , M ) and H I , J i ( M ) are studied, and it is proved that S - depth ( I , J , M ) = inf { i : H I , J i ( M ) S } , where S is a Serre subcategory closed under taking injective hulls. Some conditions are provided that local cohomology...

Matlis dual of local cohomology modules

Batoul Naal, Kazem Khashyarmanesh (2020)

Czechoslovak Mathematical Journal

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Let ( R , 𝔪 ) be a commutative Noetherian local ring, 𝔞 be an ideal of R and M a finitely generated R -module such that 𝔞 M M and cd ( 𝔞 , M ) - grade ( 𝔞 , M ) 1 , where cd ( 𝔞 , M ) is the cohomological dimension of M with respect to 𝔞 and grade ( 𝔞 , M ) is the M -grade of 𝔞 . Let D ( - ) : = Hom R ( - , E ) be the Matlis dual functor, where E : = E ( R / 𝔪 ) is the injective hull of the residue field R / 𝔪 . We show that there exists the following long exact sequence 0 H 𝔞 n - 2 ( D ( H 𝔞 n - 1 ( M ) ) ) H 𝔞 n ( D ( H 𝔞 n ( M ) ) ) D ( M ) H 𝔞 n - 1 ( D ( H 𝔞 n - 1 ( M ) ) ) H 𝔞 n + 1 ( D ( H 𝔞 n ( M ) ) ) H 𝔞 n ( D ( H ( x 1 , ... , x n - 1 ) n - 1 ( M ) ) ) H 𝔞 n ( D ( H ( n - 1 M ) ) ) ... , where n : = cd ( 𝔞 , M ) is a non-negative integer, x 1 , ... , x n - 1 is a regular sequence in 𝔞 on M and, for an R -module L , H 𝔞 i ( L ) is the i th local cohomology module...

On the real X -ranks of points of n ( ) with respect to a real variety X n

Edoardo Ballico (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let  X n be an integral and non-degenerate m -dimensional variety defined over . For any P n ( ) the real X -rank r X , ( P ) is the minimal cardinality of S X ( ) such that P S . Here we extend to the real case an upper bound for the X -rank due to Landsberg and Teitler.

On the endomorphism ring and Cohen-Macaulayness of local cohomology defined by a pair of ideals

Thiago H. Freitas, Victor H. Jorge Pérez (2019)

Czechoslovak Mathematical Journal

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Let 𝔞 , I , J be ideals of a Noetherian local ring ( R , 𝔪 , k ) . Let M and N be finitely generated R -modules. We give a generalized version of the Duality Theorem for Cohen-Macaulay rings using local cohomology defined by a pair of ideals. We study the behavior of the endomorphism rings of H I , J t ( M ) and D ( H I , J t ( M ) ) , where t is the smallest integer such that the local cohomology with respect to a pair of ideals is nonzero and D ( - ) : = Hom R ( - , E R ( k ) ) is the Matlis dual functor. We show that if R is a d -dimensional complete Cohen-Macaulay...

The general rigidity result for bundles of A -covelocities and A -jets

Jiří M. Tomáš (2017)

Czechoslovak Mathematical Journal

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Let M be an m -dimensional manifold and A = 𝔻 k r / I = N A a Weil algebra of height r . We prove that any A -covelocity T x A f T x A * M , x M is determined by its values over arbitrary max { width A , m } regular and under the first jet projection linearly independent elements of T x A M . Further, we prove the rigidity of the so-called universally reparametrizable Weil algebras. Applying essentially those partial results we give the proof of the general rigidity result T A * M T r * M without coordinate computations, which improves and generalizes the partial...

Chen–Ruan Cohomology of 1 , n and ¯ 1 , n

Nicola Pagani (2013)

Annales de l’institut Fourier

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In this work we compute the Chen–Ruan cohomology of the moduli spaces of smooth and stable n -pointed curves of genus 1 . In the first part of the paper we study and describe stack theoretically the twisted sectors of 1 , n and ¯ 1 , n . In the second part, we study the orbifold intersection theory of ¯ 1 , n . We suggest a definition for an orbifold tautological ring in genus 1 , which is a subring of both the Chen–Ruan cohomology and of the stringy Chow ring.

𝒞 k -regularity for the ¯ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

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Let D be a 𝒞 d q -convex intersection, d 2 , 0 q n - 1 , in a complex manifold X of complex dimension n , n 2 , and let E be a holomorphic vector bundle of rank N over X . In this paper, 𝒞 k -estimates, k = 2 , 3 , , , for solutions to the ¯ -equation with small loss of smoothness are obtained for E -valued ( 0 , s ) -forms on D when n - q s n . In addition, we solve the ¯ -equation with a support condition in 𝒞 k -spaces. More precisely, we prove that for a ¯ -closed form f in 𝒞 0 , q k ( X D , E ) , 1 q n - 2 , n 3 , with compact support and for ε with 0 < ε < 1 there...

Batalin-Vilkovisky algebra structures on Hochschild cohomology

Luc Menichi (2009)

Bulletin de la Société Mathématique de France

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Let M be any compact simply-connected oriented d -dimensional smooth manifold and let 𝔽 be any field. We show that the Gerstenhaber algebra structure on the Hochschild cohomology on the singular cochains of M , H H * ( S * ( M ) , S * ( M ) ) , extends to a Batalin-Vilkovisky algebra. Such Batalin-Vilkovisky algebra was conjectured to exist and is expected to be isomorphic to the Batalin-Vilkovisky algebra on the free loop space homology on M , H * + d ( L M ) introduced by Chas and Sullivan. We also show that the negative cyclic...

On 1 -cocycles induced by a positive definite function on a locally compact abelian group

Jordan Franks, Alain Valette (2014)

Annales mathématiques Blaise Pascal

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For ϕ a normalized positive definite function on a locally compact abelian group G , let π ϕ be the unitary representation associated to ϕ by the GNS construction. We give necessary and sufficient conditions for the vanishing of 1-cohomology H 1 ( G , π ϕ ) and reduced 1-cohomology H ¯ 1 ( G , π ϕ ) . For example, H ¯ 1 ( G , π ϕ ) = 0 if and only if either Hom ( G , ) = 0 or μ ϕ ( 1 G ) = 0 , where 1 G is the trivial character of G and μ ϕ is the probability measure on the Pontryagin dual G ^ associated to ϕ by Bochner’s Theorem. This streamlines an argument of Guichardet...

On lifts of projectable-projectable classical linear connections to the cotangent bundle

Anna Bednarska (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We describe all 2 m 1 , m 2 , n 1 , n 2 -natural operators D : Q p r o j - p r o j τ Q T * transforming projectable-projectable classical torsion-free linear connections on fibred-fibred manifolds Y into classical linear connections D ( ) on cotangent bundles T * Y of Y . We show that this problem can be reduced to finding 2 m 1 , m 2 , n 1 , n 2 -natural operators D : Q p r o j - p r o j τ ( T * , p T * q T ) for p = 2 , q = 1 and p = 3 , q = 0 .

On the Configuration Spaces of Grassmannian Manifolds

Sandro Manfredini, Simona Settepanella (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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Let h i ( k , n ) be the i -th ordered configuration space of all distinct points H 1 , ... , H h in the Grassmannian G r ( k , n ) of k -dimensional subspaces of n , whose sum is a subspace of dimension i . We prove that h i ( k , n ) is (when non empty) a complex submanifold of G r ( k , n ) h of dimension i ( n - i ) + h k ( i - k ) and its fundamental group is trivial if i = m i n ( n , h k ) , h k n and n &gt; 2 and equal to the braid group of the sphere P 1 if n = 2 . Eventually we compute the fundamental group in the special case of hyperplane arrangements, i.e. k = n - 1 .

Cominimaxness of local cohomology modules

Moharram Aghapournahr (2019)

Czechoslovak Mathematical Journal

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Let R be a commutative Noetherian ring, I an ideal of R . Let t 0 be an integer and M an R -module such that Ext R i ( R / I , M ) is minimax for all i t + 1 . We prove that if H I i ( M ) is FD 1 (or weakly Laskerian) for all i < t , then the R -modules H I i ( M ) are I -cominimax for all i < t and Ext R i ( R / I , H I t ( M ) ) is minimax for i = 0 , 1 . Let N be a finitely generated R -module. We prove that Ext R j ( N , H I i ( M ) ) and Tor j R ( N , H I i ( M ) ) are I -cominimax for all i and j whenever M is minimax and H I i ( M ) is FD 1 (or weakly Laskerian) for all i .

Thompson’s conjecture for the alternating group of degree 2 p and 2 p + 1

Azam Babai, Ali Mahmoudifar (2017)

Czechoslovak Mathematical Journal

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For a finite group G denote by N ( G ) the set of conjugacy class sizes of G . In 1980s, J. G. Thompson posed the following conjecture: If L is a finite nonabelian simple group, G is a finite group with trivial center and N ( G ) = N ( L ) , then G L . We prove this conjecture for an infinite class of simple groups. Let p be an odd prime. We show that every finite group G with the property Z ( G ) = 1 and N ( G ) = N ( A i ) is necessarily isomorphic to A i , where i { 2 p , 2 p + 1 } .

On the Picard number of divisors in Fano manifolds

Cinzia Casagrande (2012)

Annales scientifiques de l'École Normale Supérieure

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Let  X be a complex Fano manifold of arbitrary dimension, and D a prime divisor in  X . We consider the image 𝒩 1 ( D , X ) of  𝒩 1 ( D ) in  𝒩 1 ( X ) under the natural push-forward of 1 -cycles. We show that ρ X - ρ D codim 𝒩 1 ( D , X ) 8 . Moreover if codim 𝒩 1 ( D , X ) 3 , then either X S × T where S is a Del Pezzo surface, or codim 𝒩 1 ( D , X ) = 3 and X has a fibration in Del Pezzo surfaces onto a Fano manifold T such that ρ X - ρ T = 4 .

A criterion for pure unrectifiability of sets (via universal vector bundle)

Silvano Delladio (2011)

Annales Polonici Mathematici

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Let m,n be positive integers such that m < n and let G(n,m) be the Grassmann manifold of all m-dimensional subspaces of ℝⁿ. For V ∈ G(n,m) let π V denote the orthogonal projection from ℝⁿ onto V. The following characterization of purely unrectifiable sets holds. Let A be an m -measurable subset of ℝⁿ with m ( A ) < . Then A is purely m-unrectifiable if and only if there exists a null subset Z of the universal bundle ( V , v ) | V G ( n , m ) , v V such that, for all P ∈ A, one has m ( n - m ) ( V G ( n , m ) | ( V , π V ( P ) ) Z ) > 0 . One can replace “for all P ∈ A” by “for...