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1.
Any algebraic surface in which is fibered in cubics, so that the generic fibre is a twisted cubic, gives rise to a curve Γ in a suitable compactification X of the space of smooth rational cubics of In this paper the case n = 4 is addressed and the corresponding space X is studied. We apply our results to complete the classification of smooth, rational surfaces in ruled in cubics. This work is within the framework of the national research project “Geometry on Algebraic Varieties” Cofin 2006 of MIUR.  相似文献   

2.
Let be a C 2 map and let Spec(Y) denote the set of eigenvalues of the derivative DY p , when p varies in . We begin proving that if, for some ϵ > 0, then the foliation with made up by the level surfaces {k = constant}, consists just of planes. As a consequence, we prove a bijectivity result related to the three-dimensional case of Jelonek’s Jacobian Conjecture for polynomial maps of The first author was supported by CNPq-Brazil Grant 306992/2003-5. The first and second author were supported by FAPESP-Brazil Grant 03/03107-9.  相似文献   

3.
We define the notion of a geometric graph in . This is a graph drawn in with its vertices drawn as points and its edges as straight line segments connecting corresponding points. We call two disjoint edges of G strongly avoiding if there exists an orthogonal projection of to a two dimensional plane H such that the projections of the two edges on H are contained in two different rays, respectively, with a common apex that create a non-acute angle. We show that a geometric graph on n vertices in with no pair of strongly avoiding edges has at most 2n − 2 edges. As a consequence we get a new proof to Vázsonyi’s conjecture about the maximum number of diameters in a set of n points in . This research was supported by THE ISRELI SCIENCE FOUNDATION (grant No. 938/06).  相似文献   

4.
In this paper, we characterize the dynamic of every Abelian subgroups of , or . We show that there exists a -invariant, dense open set U in saturated by minimal orbits with a union of at most n -invariant vector subspaces of of dimension n−1 or n−2 over . As a consequence, has height at most n and in particular it admits a minimal set in . This work is supported by the research unit: systèmes dynamiques et combinatoire: 99UR15-15  相似文献   

5.
Laguerre geometry of surfaces in is given in the book of Blaschke [Vorlesungen über Differentialgeometrie, Springer, Berlin Heidelberg New York (1929)], and has been studied by Musso and Nicolodi [Trans. Am. Math. soc. 348, 4321–4337 (1996); Abh. Math. Sem. Univ. Hamburg 69, 123–138 (1999); Int. J. Math. 11(7), 911–924 (2000)], Palmer [Remarks on a variation problem in Laguerre geometry. Rendiconti di Mathematica, Serie VII, Roma, vol. 19, pp. 281–293 (1999)] and other authors. In this paper we study Laguerre differential geometry of hypersurfaces in . For any umbilical free hypersurface with non-zero principal curvatures we define a Laguerre invariant metric g on M and a Laguerre invariant self-adjoint operator : TM → TM, and show that is a complete Laguerre invariant system for hypersurfaces in with n≥ 4. We calculate the Euler–Lagrange equation for the Laguerre volume functional of Laguerre metric by using Laguerre invariants. Using the Euclidean space , the semi-Euclidean space and the degenerate space we define three Laguerre space forms , and and define the Laguerre embeddings and , analogously to what happens in the Moebius geometry where we have Moebius space forms S n , and (spaces of constant curvature) and conformal embeddings and [cf. Liu et al. in Tohoku Math. J. 53, 553–569 (2001) and Wang in Manuscr. Math. 96, 517–534 (1998)]. Using these Laguerre embeddings we can unify the Laguerre geometry of hypersurfaces in , and . As an example we show that minimal surfaces in or are Laguerre minimal in .C. Wang Partially supported by RFDP and Chuang-Xin-Qun-Ti of NSFC.  相似文献   

6.
In this article we extend Milnor’s fibration theorem to the case of functions of the form with f, g holomorphic, defined on a complex analytic (possibly singular) germ (X, 0). We further refine this fibration theorem by looking not only at the link of , but also at its multi-link structure, which is more subtle. We mostly focus on the case when X has complex dimension two. Our main result (Theorem 4.4) gives in this case the equivalence of the following three statements:
(i)  The real analytic germ has 0 as an isolated critical value;
(ii)  the multilink is fibered; and
(iii)  if is a resolution of the holomorphic germ , then for each rupture vertex (j) of the decorated dual graph of π one has that the corresponding multiplicities of f, g satisfy: .
Moreover one has that if these conditions hold, then the Milnor-Lê fibration of is a fibration of the multilink . We also give a combinatorial criterium to decide whether or not the multilink is fibered. If the meromorphic germ f/g is semitame, then we show that the Milnor-Lê fibration given by is equivalent to the usual Milnor fibration given by . We finish this article by discussing several realization problems. Research partially supported by CONACYT and DGAPA-UNAM, Mexico, and by CNRS and ECOS, France.  相似文献   

7.
Suppose M is a tracial von Neumann algebra embeddable into (the ultraproduct of the hyperfinite II1-factor) and X is an n-tuple of selfadjoint generators for M. Denote by Γ(X; m, k, γ) the microstate space of X of order (m, k ,γ). We say that X is tubular if for any ε >  0 there exist and γ > 0 such that if then there exists a k × k unitary u satisfying for each 1 ≤  i ≤  n. We show that the following conditions are equivalent:
•  M is amenable (i.e., injective).
•  X is tubular.
•  Any two embeddings of M into are conjugate by a unitary .
Research supported in part by the NSF. Dedicated to Ed Effros on the occasion of his 70th birthday.  相似文献   

8.
Given a hypersurface M of null scalar curvature in the unit sphere , n ≥ 4, such that its second fundamental form has rank greater than 2, we construct a singular scalar-flat hypersurface in as a normal graph over a truncated cone generated by M. Furthermore, this graph is 1-stable if the cone is strictly 1-stable.  相似文献   

9.
We study the existence of different types of positive solutions to problem
where , , and is the critical Sobolev exponent. A careful analysis of the behavior of Palais-Smale sequences is performed to recover compactness for some ranges of energy levels and to prove the existence of ground state solutions and mountain pass critical points of the associated functional on the Nehari manifold. A variational perturbative method is also used to study the existence of a non trivial manifold of positive solutions which bifurcates from the manifold of solutions to the uncoupled system corresponding to the unperturbed problem obtained for ν = 0. B. Abdellaoui and I. Peral supported by projects MTM2007-65018, MEC and CCG06-UAM/ESP-0340, Spain. V. Felli supported by Italy MIUR, national project Variational Methods and Nonlinear Differential Equations.  相似文献   

10.
It is known that in the moduli space of elliptic curves, there exist precisely nine -rational points represented by an elliptic curve with complex multiplication by the maximal order of an imaginary quadratic field. In Murabayashi and Umegaki (J Algebra 235:267–274, 2001) and Umegaki [Determination of all -rational CM-points in the moduli spaces of polarized abelian surfaces, Analytic number theory (Beijng/Kyoto, 1999). Dev. Math., vol 6. Kluwer, Dordrecht, pp 349–357, 2002] we determined all -rational points in (the moduli space of d-polarized abelian surfaces) represented by a d-polarized abelian surface whose endomorphism ring is isomorphic to the maximal order of a quartic CM-field by using the result in Murabayashi (J Reine Angew Math 470:1–26, 1996). In this paper, we prove that polarized abelian surfaces corresponding to these -rational CM points have a -rational model by constructing certain Hecke characters.  相似文献   

11.
It has been known for a long time that the Deligne–Lusztig curves associated to the algebraic groups of type and defined over the finite field all have the maximum number of -rational points allowed by the Weil “explicit formulas”, and that these curves are -maximal curves over infinitely many algebraic extensions of . Serre showed that an -rational curve which is -covered by an -maximal curve is also -maximal. This has posed the problem of the existence of -maximal curves other than the Deligne–Lusztig curves and their -subcovers, see for instance Garcia (On curves with many rational points over finite fields. In: Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, pp. 152–163. Springer, Berlin, 2002) and Garcia and Stichtenoth (A maximal curve which is not a Galois subcover of the Hermitan curve. Bull. Braz. Math. Soc. (N.S.) 37, 139–152, 2006). In this paper, a positive answer to this problem is obtained. For every q = n 3 with n = p r  > 2, p ≥ 2 prime, we give a simple, explicit construction of an -maximal curve that is not -covered by any -maximal Deligne–Lusztig curve. Furthermore, the -automorphism group Aut has size n 3(n 3 + 1)(n 2 − 1)(n 2 − n + 1). Interestingly, has a very large -automorphism group with respect to its genus . Research supported by the Italian Ministry MURST, Strutture geometriche, combinatoria e loro applicazioni, PRIN 2006–2007.  相似文献   

12.
13.
We classify the solutions to the equation (−Δ) m u = (2m − 1)!e 2mu on giving rise to a metric with finite total Q-curvature in terms of analytic and geometric properties. The analytic conditions involve the growth rate of u and the asymptotic behaviour of Δu at infinity. As a consequence we give a geometric characterization in terms of the scalar curvature of the metric at infinity, and we observe that the pull-back of this metric to S 2m via the stereographic projection can be extended to a smooth Riemannian metric if and only if it is round.  相似文献   

14.
We show a way to choose nice coordinates on a surface in and use this to study minimal surfaces. We show that only open parts of cylinders over a geodesic in are both minimal and flat. We also show that the condition that the projection of the direction tangent to onto the tangent space of the surface is a principal direction, is equivalent to the condition that the surface is normally flat in . We present classification theorems under the extra assumption of minimality or flatness. J. Fastenakels is a research assistant of the Research Foundation—Flanders (FWO). J. Van der Veken is a postdoctoral researcher supported by the Research Foundation—Flanders (FWO). This work was partially supported by project G.0432.07 of the Research Foundation—Flanders (FWO).  相似文献   

15.
We consider the following Liouville equation in
For each fixed and a j  > 0 for 1 ≤ jk, we construct a solution to the above equation with the following asymptotic behavior:
  相似文献   

16.
Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex hyperbolic space with any specified value of the Hopf principal curvature α less than or equal to the corresponding value for the horosphere. We give a construction for all such hypersurfaces in terms of Weierstrass-type data, and also obtain a classification of pseudo-Einstein hypersurfaces in .   相似文献   

17.
We study permanence properties of the classes of stable and so-called -stable -algebras, respectively. More precisely, we show that a (X)-algebra A is stable if all its fibres are, provided that the underlying compact metrizable space X has finite covering dimension or that the Cuntz semigroup of A is almost unperforated (a condition which is automatically satisfied for -algebras absorbing the Jiang–Su algebra tensorially). Furthermore, we prove that if is a K 1-injective strongly self-absorbing -algebra, then A absorbs tensorially if and only if all its fibres do, again provided that X is finite-dimensional. This latter statement generalizes results of Blanchard and Kirchberg. We also show that the condition on the dimension of X cannot be dropped. Along the way, we obtain a useful characterization of when a -algebra with weakly unperforated Cuntz semigroup is stable, which allows us to show that stability passes to extensions of -absorbing -algebras. Research supported by: Deutsche Forschungsgemeinschaft (through the SFB 478), by the EU-Network Quantum Spaces - Noncommutative Geometry (Contract No. HPRN-CT-2002-00280), and by the Center for Advanced Studies in Mathematics at Ben-Gurion University  相似文献   

18.
It is shown that an elliptic scattering operator A on a compact manifold with boundary with operator valued coefficients in the morphisms of a bundle of Banach spaces of class () and Pisier’s property (α) has maximal regularity (up to a spectral shift), provided that the spectrum of the principal symbol of A on the scattering cotangent bundle avoids the right half-plane. This is accomplished by representing the resolvent in terms of pseudodifferential operators with -bounded symbols, yielding by an iteration argument the -boundedness of λ(A−λ)−1 in for some . To this end, elements of a symbolic and operator calculus of pseudodifferential operators with -bounded symbols are introduced. The significance of this method for proving maximal regularity results for partial differential operators is underscored by considering also a more elementary situation of anisotropic elliptic operators on with operator valued coefficients.  相似文献   

19.
Suppose is affine surface measure on a convex radial surface Γ(x) = (x, γ(|x|)), a ≤ |x| < b, in . Under appropriate smoothness and growth conditions on γ, we prove and Fourier restriction estimates for Γ.  相似文献   

20.
We study the functional codes of second order on a non-degenerate Hermitian variety as defined by G. Lachaud. We provide the best possible bounds for the number of points of quadratic sections of . We list the first five weights, describe the corresponding codewords and compute their number. The paper ends with two conjectures. The first is about minimum distance of the functional codes of order h on a non-singular Hermitian variety . The second is about distribution of the codewords of first five weights of the functional codes of second order on a non-singular Hermitian variety .   相似文献   

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