共查询到20条相似文献,搜索用时 46 毫秒
1.
Hao Sun 《Mathematische Zeitschrift》2014,277(3-4):739-747
In this paper we prove that for any smooth projective variety of Albanese fiber dimension two and of general type, the \(6\) -canonical map is birational. And we also show that the \(5\) -canonical map is birational for any such variety with some geometric restrictions. 相似文献
2.
Dan Abramovich Kalle Karu Kenji Matsuki Jaroslaw Wlodarczyk 《Journal of the American Mathematical Society》2002,15(3):531-572
Building on work of the fourth author and Morelli's work, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field of characteristic zero is a composite of blowings up and blowings down with nonsingular centers.
3.
We first prove that any birational map, from an affine space of dimension ≥ 2 to itself, is not determined by its face functions.
On the other hand, we prove that a birational map with irreducibly polynomial inverse is completely determined, within the
class of all birational maps with irreducibly polynomial inverses, by its face functions. We show also how to effectively
reconstruct such a map from its face functions.
Supported partly by the Centre Interuniversitaireen Calcul Mathématique Algébrique. 相似文献
4.
Francisco Javier Gallego Miguel González Bangere P. Purnaprajna 《Inventiones Mathematicae》2010,182(1):1-46
In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties
with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite map can
be deformed to a one-to-one map. We use this criterion to construct new surfaces of general type with birational canonical
map, for different c12c_{1}^{2} and χ (the canonical map of the surfaces we construct is in fact a finite, birational morphism). Our general results enable us
to describe some new components of the moduli of surfaces of general type. We also find infinitely many moduli spaces having one component whose general point corresponds to a canonically embedded surface and another component whose general
point corresponds to a surface whose canonical map is a degree 2 morphism. 相似文献
5.
Ernesto C. Mistretta 《Mathematische Nachrichten》2020,293(11):2175-2186
A generically generated vector bundle on a smooth projective variety yields a rational map to a Grassmannian, called Kodaira map. We answer a previous question, raised by the asymptotic behaviour of such maps, giving rise to a birational characterization of abelian varieties. In particular we prove that, under the conjectures of the Minimal Model Program, a smooth projective variety is birational to an abelian variety if and only if it has Kodaira dimension 0 and some symmetric power of its cotangent sheaf is generically generated by its global sections. 相似文献
6.
We prove that the moduli space X(1,7) of (1,7)–polarized abelian surfaces with canonical level–structure is birational to the Fano 3–fold V22 of polar hexagons of the Klein quartic (7). In particular X(1,7) is rational and the birational map to ℙ3 is defined over ℚ. As a byproduct we obtain explicitely the equations of the (1,7)–very–ample–polarized abelian surfaces embedded in ℙ6. 相似文献
7.
8.
Let X be a smooth complex projective algebraic variety of maximal Albanese dimension. We give a characterization of in terms of the set . An immediate consequence of this is that the Kodaira dimension is invariant under smooth deformations. We then study the pluricanonical maps . We prove that if X is of general type, is generically finite for and birational for . More generally, we show that for the image of is of dimension equal to and for , is the stable canonical map.
Received July 7, 2000 / Published online April 12, 2001 相似文献
9.
Using polar conics of plane cubics we define a rational map from the moduli space of stable binary sextics into the moduli space of Desargues configurations. We show that this map is the inverse of a birational map defined via the von Staudt conic. In particular Ψ
m
is a birational map. 相似文献
10.
We construct the Green current for a random iteration of horizontal-like mappings in . This is applied to the study of a polynomial map with the following properties:
i. infinity is f-attracting;
ii. f contracts the line at infinity to a point not in the indeterminacy set.
We study for such mappings the escape rates near infinity, i.e. the set of possible values of the function We show in particular that the set of possible values can contain an interval.
On the other hand the Green current T of f can be decomposed into pieces associated to an itinerary defined by the indeterminacy points. This allows us to prove that
exists ||T||-a.e. and we give its value in terms of explicit quantities depending on f. 相似文献
11.
《代数通讯》2013,41(7):2961-2976
The aim of this paper is to study varieties with second Gauss map not birational. In particular we classify such varieties in dimension two. We prove that there are two types of surfaces S of P n (C), with n > 5, not satisfying Laplace equations, with second Gauss map t 2 not birational: i. surfaces such that the image of the second Gauss map is one-dimensional and containing a one-dimensional family of curves. Each curve of the family is contained in some P 3 ? P n . ii. surfaces such that the second Gauss map is generically finite of degree at least two. In this case the image of the second Gauss map is two-dimensional, locally embedded in a Laplace congruence and meeting the general generatrix in more than one point. 相似文献
12.
Huaibin Li 《印度理论与应用数学杂志》2013,44(6):849-863
In this paper, we consider a rational map f of degree at least two acting on Riemman sphere that is expanding away from critical points. Assuming that all critical points of f in the Julia set J(f) are reluctantly recurrent, we prove that the Hausdorff dimension of the Julia set J(f) is equal to the hyperbolic dimension, and the Lebesgue measure of Julia set is zero when the Julia set J(f) ≠ . 相似文献
13.
Anna Zdunik 《Inventiones Mathematicae》1997,128(2):303-327
For a generalized polynomial-like mapping we prove the existence of an invariant ergodic measure equivalent to the harmonic
measure on the Julia set J( f).
We also prove that for polynomial-like mappings the harmonic measure is equivalent to the maximal entropy measure iff f is conformally equivalent to a polynomial.
Next, we show that the Hausdorff dimension of harmonic measure on the Julia set of a generalized polynomial-like map is strictly
smaller than 1 unless the Julia set is connected.
Oblatum 24-IV-1995 & 22-VII-1996 相似文献
14.
T.J Lyons 《Journal of Functional Analysis》1980,37(1):19-26
Consider the map from the fine interior of a compact set to the measures on the fine boundary given by Balayage of the unit point mass onto the fine boundary (the Keldych measure). It is shown that for any point in the domain there is a compact fine neighborhood of the point on which the map is continuous from the initial topology on the compact set to the norm topology on measures. In this paper we only prove a rather special case, the method could easily be generalized to more abstract potential spaces. One consequence of this result is a Hartog-type theorem for finely harmonic functions. We use the Hartog theorem, rational approximation theory, and results proved in a previous paper by the author to prove that the derivative of a finely holomorphic function exists everywhere and is finely holomorphic. 相似文献
15.
Michela Artebani 《Transactions of the American Mathematical Society》2008,360(3):1581-1599
S. Kondo used periods of surfaces to prove that the moduli space of genus three curves is birational to an arithmetic quotient of a complex 6-ball. In this paper we study Heegner divisors in the ball quotient, given by arithmetically defined hyperplane sections of the ball. We show that the corresponding loci of genus three curves are given by hyperelliptic curves, singular plane quartics and plane quartics admitting certain rational ``splitting curves'.
16.
本又考虑Lauwerier映射Fa,b(x,y)=(bx(1-2y)+y,ay(1-y)).我们证明对于参数α在一个正测度集合中,对应的映射有非平凡的拓扑可迁的吸引子,其中是某个双曲不动点的不稳定集的闭包.周期点是双曲的且在中稠密,而且中任两个周期点异宿相关(稳定与不稳定集的横截相交).同时也构造支撑在吸引子上的Sinal-Bowen-Ruelle测度,并研究其性质. 相似文献
17.
Mathematische Zeitschrift - A simple birational map is a K-equivalent birational map which is resolved by a single blowing-up. Examples of such maps include standard flops and twisted Mukai flops.... 相似文献
18.
Margarida Mendes Lopes Rita Pardini Sofia Tirabassi 《Mathematische Nachrichten》2023,296(10):4739-4744
Kawamata has shown that the quasi-Albanese map of a quasi-projective variety with log-irregularity equal to the dimension and log-Kodaira dimension 0 is birational. In this note, we show that under these hypotheses the quasi-Albanese map is proper in codimension 1 as conjectured by Iitaka. 相似文献
19.
FENGJINGHAI 《高校应用数学学报(英文版)》1997,12(3):363-370
In this paper, we will discuss the constructiOn problems about the invariant sets and invariant measures of continues maps~ which map complexes into themselves, using simplical approximation and Markov cbeirs. In [7], the author defined a matrix by using r-normal subdivi of the w,dimensional unit cube, considered it a Markov matrix, and constructed the invariantset and invafiant measure, In fact, the matrix he defined is not Markov matrix generally. So wewill give [7] and amendment in the last pert of this paper. We also construct an invariant set thatis the chain-recurrent set of the map by means of a non-negative matrix which only depends on themap. At hst, we will prove the higher dimension?Banach variation formuls that can simplify thetransition matrix. 相似文献
20.
Kei Funano 《Geometriae Dedicata》2007,127(1):49-56
The property of measure concentration is that an arbitrary 1-Lipschitz function on an mm-space X is almost close to a constant function. In this paper, we prove that if such a concentration phenomenon arise, then any 1-Lipschitz
map f from X to a space Y with a doubling measure also concentrates to a constant map. As a corollary, we get any 1-Lipschitz map to a Riemannian manifold
with a lower Ricci curvature bounds also concentrates to a constant map.
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