-dimension function of bitopological spaces
M. Jelić (1987)
Matematički Vesnik
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M. Jelić (1987)
Matematički Vesnik
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Yasunao Hattori, Jan van Mill (2013)
Bulletin of the Polish Academy of Sciences. Mathematics
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We prove that , where trt stands for the transfinite extension of Steinke’s separation dimension. This answers a question of Chatyrko and Hattori.
Margarida Mendes Lopes, Rita Pardini, Pietro Pirola (2014)
Journal of the European Mathematical Society
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We take up the study of the Brill-Noether loci , where is a smooth projective variety of dimension , , and is an integer. By studying the infinitesimal structure of these loci and the Petri map (defined in analogy with the case of curves), we obtain lower bounds for , where is a divisor that moves linearly on a smooth projective variety of maximal Albanese dimension. In this way we sharpen the results of [Xi] and we generalize them to dimension . In the -dimensional case...
Jun-Muk Hwang (2013)
Annales scientifiques de l'École Normale Supérieure
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Let be a uniruled projective manifold and let be a general point. The main result of [2] says that if the -degrees (i.e., the degrees with respect to the anti-canonical bundle of ) of all rational curves through are at least , then is a projective space. In this paper, we study the structure of when the -degrees of all rational curves through are at least . Our study uses the projective variety , called the VMRT at , defined as the union of tangent directions to the...
Michael Levin (2003)
Fundamenta Mathematicae
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We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dimension ≤ n+1 and a surjective -map r: Z → X such that for every abelian group G and every integer k ≥ 2 such that we have and r is G-acyclic.
Jürgen Leiterer (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Let be a holomorphic Banach bundle over a compact complex manifold, which can be defined by a cocycle of holomorphic transition functions with values of the form where is compact. Assume that the characteristic fiber of has the compact approximation property. Let be the complex dimension of and . Then: If is a holomorphic vector bundle (of finite rank) with , then . In particular, if , then .
Nicolas Monod, Henrik Densing Petersen (2014)
Annales de l’institut Fourier
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Let be any group containing an infinite elementary amenable subgroup and let . We construct an exhaustion of by closed invariant subspaces which all intersect trivially a fixed non-trivial closed invariant subspace. This is an obstacle to -dimension and gives an answer to a question of Gaboriau.
Aiping Zhang, Xueping Lei (2024)
Czechoslovak Mathematical Journal
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Let be a CM-finite Artin algebra with a Gorenstein-Auslander generator , be a Gorenstein projective -module and . We give an upper bound for the finitistic dimension of in terms of homological data of . Furthermore, if is -Gorenstein for , then we show the global dimension of is less than or equal to plus the -projective dimension of As an application, the global dimension of is less than or equal to .
Ludwik Jaksztas (2011)
Fundamenta Mathematicae
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Let f₀(z) = z²+1/4. We denote by ₀ the set of parameters σ ∈ ℂ for which the critical point 0 escapes from the filled-in Julia set K(f₀) in one step by the Lavaurs map . We prove that if σ₀ ∈ ∂₀, then the Hausdorff dimension of the Julia-Lavaurs set is continuous at σ₀ as the function of the parameter if and only if . Since on a dense set of parameters which correspond to preparabolic points, the lower semicontinuity implies the continuity of on an open and dense subset of...
Ludwik Jaksztas (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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This paper is motivated by the problem of dependence of the Hausdorff dimension of the Julia-Lavaurs sets for the map f₀(z) = z²+1/4 on the parameter σ. Using homographies, we imitate the construction of the iterated function system (IFS) whose limit set is a subset of , given by Urbański and Zinsmeister. The closure of the limit set of our IFS is the closure of some family of circles, and if the parameter σ varies, then the behavior of the limit set is similar to the behavior of...
H. Murat Tuncali, Vesko Valov (2002)
Fundamenta Mathematicae
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Let f: X → Y be a closed n-dimensional surjective map of metrizable spaces. It is shown that if Y is a C-space, then: (1) the set of all maps g: X → ⁿ with dim(f △ g) = 0 is uniformly dense in C(X,ⁿ); (2) for every 0 ≤ k ≤ n-1 there exists an -subset of X such that and the restriction is (n-k-1)-dimensional. These are extensions of theorems by Pasynkov and Toruńczyk, respectively, obtained for finite-dimensional spaces. A generalization of a result due to Dranishnikov and Uspenskij...
Jungkai A. Chen, Meng Chen (2010)
Annales scientifiques de l'École Normale Supérieure
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Let be a complex nonsingular projective 3-fold of general type. We prove and for some positive integer . A direct consequence is the birationality of the pluricanonical map for all . Besides, the canonical volume has a universal lower bound .
Viktor Petrov, Nikita Semenov, Kirill Zainoulline (2008)
Annales scientifiques de l'École Normale Supérieure
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Let be a semisimple linear algebraic group of inner type over a field , and let be a projective homogeneous -variety such that splits over the function field of . We introduce the -invariant of which characterizes the motivic behavior of , and generalizes the -invariant defined by A. Vishik in the context of quadratic forms. We use this -invariant to provide motivic decompositions of all generically split projective homogeneous -varieties, e.g. Severi-Brauer varieties,...
Chun-Yun Cao, Bao-Wei Wang, Jun Wu (2013)
Studia Mathematica
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Let be an infinite iterated function system on [0,1] satisfying the open set condition with the open set (0,1) and let Λ be its attractor. Then to any x ∈ Λ (except at most countably many points) corresponds a unique sequence of integers, called the digit sequence of x, such that . We investigate the growth speed of the digits in a general infinite iterated function system. More precisely, we determine the dimension of the set for any infinite subset B ⊂ ℕ, a question posed by...
Włodzimierz M. Mikulski (2024)
Archivum Mathematicum
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We classify classical linear connections on the total space of a fibred manifold induced in a natural way by the following three objects: a general connection in , a classical linear connection on and a linear connection in the vertical bundle . The main result says that if and then the natural operators under consideration form the dimensional affine space.
Fan Lü, Bo Tan, Jun Wu (2014)
Fundamenta Mathematicae
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For x ∈ (0,1), the univoque set for x, denoted (x), is defined to be the set of β ∈ (1,2) such that x has only one representation of the form x = x₁/β + x₂/β² + ⋯ with . We prove that for any x ∈ (0,1), (x) contains a sequence increasing to 2. Moreover, (x) is a Lebesgue null set of Hausdorff dimension 1; both (x) and its closure are nowhere dense.
Vincenzo Di Gennaro, Davide Franco (2009)
Annales scientifiques de l'École Normale Supérieure
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Let be an -dimensional irreducible smooth complex projective variety embedded in a projective space. Let be a closed subscheme of , and be a positive integer such that is generated by global sections. Fix an integer , and assume the general divisor is smooth. Denote by the quotient of by the cohomology of and also by the cycle classes of the irreducible components of dimension of . In the present paper we prove that the monodromy representation on for the family...
Olivier Debarre (2006)
Bulletin de la Société Mathématique de France
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To any finite covering of degree between smooth complex projective manifolds, one associates a vector bundle of rank on whose total space contains . It is known that is ample when is a projective space ([Lazarsfeld 1980]), a Grassmannian ([Manivel 1997]), or a Lagrangian Grassmannian ([Kim Maniel 1999]). We show an analogous result when is a simple abelian variety and does not factor through any nontrivial isogeny . This result is obtained by showing that is -regular...
Ilya Tyomkin (2013)
Journal of the European Mathematical Society
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In the current paper we show that the dimension of a family of irreducible reduced curves in a given ample linear system on a toric surface over an algebraically closed field is bounded from above by , where denotes a general curve in the family. This result generalizes a famous theorem of Zariski to the case of positive characteristic. We also explore new phenomena that occur in positive characteristic: We show that the equality does not imply the nodality of even if belongs...
Juan Rivera-Letelier (2001)
Fundamenta Mathematicae
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Given d ≥ 2 consider the family of polynomials for c ∈ ℂ. Denote by the Julia set of and let be the connectedness locus; for d = 2 it is called the Mandelbrot set. We study semihyperbolic parameters : those for which the critical point 0 is not recurrent by and without parabolic cycles. The Hausdorff dimension of , denoted by , does not depend continuously on c at such ; on the other hand the function is analytic in . Our first result asserts that there is still some...
Cinzia Casagrande (2012)
Annales scientifiques de l'École Normale Supérieure
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Let be a complex Fano manifold of arbitrary dimension, and a prime divisor in . We consider the image of in under the natural push-forward of -cycles. We show that . Moreover if , then either where is a Del Pezzo surface, or and has a fibration in Del Pezzo surfaces onto a Fano manifold such that .