Displaying similar documents to “Semistability of Frobenius direct images over curves”

Equivalence bundles over a finite group and strong Morita equivalence for unital inclusions of unital C * -algebras

Kazunori Kodaka (2022)

Mathematica Bohemica

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Let 𝒜 = { A t } t G and = { B t } t G be C * -algebraic bundles over a finite group G . Let C = t G A t and D = t G B t . Also, let A = A e and B = B e , where e is the unit element in G . We suppose that C and D are unital and A and B have the unit elements in C and D , respectively. In this paper, we show that if there is an equivalence 𝒜 - -bundle over G with some properties, then the unital inclusions of unital C * -algebras A C and B D induced by 𝒜 and are strongly Morita equivalent. Also, we suppose that 𝒜 and are saturated and that A ' C = 𝐂 1 . We show that...

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...

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 .

Steinness of bundles with fiber a Reinhardt bounded domain

Karl Oeljeklaus, Dan Zaffran (2006)

Bulletin de la Société Mathématique de France

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Let E denote a holomorphic bundle with fiber D and with basis B . Both D and B are assumed to be Stein. For D a Reinhardt bounded domain of dimension d = 2 or 3 , we give a necessary and sufficient condition on D for the existence of a non-Stein such E (Theorem 1 ); for d = 2 , we give necessary and sufficient criteria for E to be Stein (Theorem 2 ). For D a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for E to be Stein (Theorem...

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...

The local lifting problem for actions of finite groups on curves

Ted Chinburg, Robert Guralnick, David Harbater (2011)

Annales scientifiques de l'École Normale Supérieure

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Let k be an algebraically closed field of characteristic p &gt; 0 . We study obstructions to lifting to characteristic 0 the faithful continuous action φ of a finite group G on k [ [ t ] ] . To each such  φ a theorem of Katz and Gabber associates an action of G on a smooth projective curve Y over k . We say that the KGB obstruction of φ vanishes if G acts on a smooth projective curve X in characteristic  0 in such a way that X / H and Y / H have the same genus for all subgroups H G . We determine for which G the KGB...

An effective proof of the hyperelliptic Shafarevich conjecture

Rafael von Känel (2014)

Journal de Théorie des Nombres de Bordeaux

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Let C be a hyperelliptic curve of genus g 1 over a number field K with good reduction outside a finite set of places S of K . We prove that C has a Weierstrass model over the ring of integers of K with height effectively bounded only in terms of g , S and K . In particular, we obtain that for any given number field K , finite set of places S of K and integer g 1 one can in principle determine the set of K -isomorphism classes of hyperelliptic curves over K of genus g with good reduction outside...

On the birational gonalities of smooth curves

E. Ballico (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let C be a smooth curve of genus g . For each positive integer r the birational r -gonality s r ( C ) of C is the minimal integer t such that there is L Pic t ( C ) with h 0 ( C , L ) = r + 1 . Fix an integer r 3 . In this paper we prove the existence of an integer g r such that for every integer g g r there is a smooth curve C of genus g with s r + 1 ( C ) / ( r + 1 ) > s r ( C ) / r , i.e. in the sequence of all birational gonalities of C at least one of the slope inequalities fails.

Sum-product theorems and incidence geometry

Mei-Chu Chang, Jozsef Solymosi (2007)

Journal of the European Mathematical Society

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In this paper we prove the following theorems in incidence geometry. 1. There is δ > 0 such that for any P 1 , , P 4 , and Q 1 , , Q n 2 , if there are n ( 1 + δ ) / 2 many distinct lines between P i and Q j for all i , j , then P 1 , , P 4 are collinear. If the number of the distinct lines is < c n 1 / 2 then the cross ratio of the four points is algebraic. 2. Given c > 0 , there is δ > 0 such that for any P 1 , P 2 , P 3 2 noncollinear, and Q 1 , , Q n 2 , if there are c n 1 / 2 many distinct lines between P i and Q j for all i , j , then for any P 2 { P 1 , P 2 , P 3 } , we have δ n distinct lines between P and Q j . 3. Given...

Involutivity degree of a distribution at superdensity points of its tangencies

Silvano Delladio (2021)

Archivum Mathematicum

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Let Φ 1 , ... , Φ k + 1 (with k 1 ) be vector fields of class C k in an open set U N + m , let 𝕄 be a N -dimensional C k submanifold of U and define 𝕋 : = { z 𝕄 : Φ 1 ( z ) , ... , Φ k + 1 ( z ) T z 𝕄 } where T z 𝕄 is the tangent space to 𝕄 at z . Then we expect the following property, which is obvious in the special case when z 0 is an interior point (relative to 𝕄 ) of 𝕋 : If z 0 𝕄 is a ( N + k ) -density point (relative to 𝕄 ) of 𝕋 then all the iterated Lie brackets of order less or equal to k Φ i 1 ( z 0 ) , [ Φ i 1 , Φ i 2 ] ( z 0 ) , [ [ Φ i 1 , Φ i 2 ] , Φ i 3 ] ( z 0 ) , ... ( h , i h k + 1 ) belong to T z 0 𝕄 . Such a property has been proved in [9] for k = 1 and its proof in the...