Mostrando recursos 1 - 20 de 1.539

  1. Good Geometry on the Curve Moduli

    Liu, Kefeng; Sun, Xiaofeng; Yau, Shing-Tung

  2. Simple Rational Polynomials and the Jacobian Conjecture

    Lê, D?ng Tráng
    Consider an algebraic map $\Phi:=(f,g):{\mathbb C}^2\rightarrow {\mathbb C}^2$ defined by the polynomial functions $f$ and $g$ of ${\mathbb C}^2$. In complex dimension $2$ the Jacobian conjecture asserts that, if the determinant $J(f,g)$ of the Jacobian matrix of $\Phi$ is a non-zero constant, then the algebraic map $\Phi$ is an isomorphism.

  3. Functoriality in Resolution of Singularities

    Bierstone, Edward; Milman, Pierre D.
    Algorithms for resolution of singularities in characteristic zero are based on Hironaka's idea of reducing the problem to a simpler question of desingularization of an ``idealistic exponent'' (or ``marked ideal''). How can we determine whether two marked ideals are equisingular in the sense that they can be resolved by the same blowing-up sequences? We show there is a desingularization functor defined on the category of equivalence classes of marked ideals and smooth morphisms, where marked ideals are ``equivalent'' if they have the same sequences of ``test transformations''. Functoriality in this sense realizes Hironaka's idealistic exponent philosophy. We use it to show that the recent algorithms for desingularization of marked ideals of...

  4. On the Density of Unnormalized Tamagawa Numbers of Orthogonal Groups I

    Hayasaka, Norihiko; Yukie, Akihiko

  5. Lattice Cohomology of Normal Surface Singularities

    Némethi, András
    For any negative definite plumbed 3-manifold $M$ we construct from its plumbed graph a graded $\Z[U]$-module. This, for rational homology spheres, conjecturally equals the Heegaard-Floer homology of Ozsváth and Szabó, but it has even more structure. If $M$ is a complex singularity link then the normalized Euler-characteristic can be compared with the analytic invariants. The Seiberg-Witten Invariant Conjecture is discussed in the light of this new object.

  6. Mordell-Weil Groups of a Hyperkähler Manifold—A Question of F. Campana

    Oguiso, Keiji
    Among other things, we show that Mordell-Weil groups of finitely many different abelian fibrations of a hyperkähler manifold have essentially no relation, as its birational transformation. Precise definition of the terms ``essentially no relation'' will be given in Introduction.

  7. Valuations and Plurisubharmonic Singularities

    Boucksom, Sébastien; Favre, Charles; Jonsson, Mattias
    We extend to higher dimensions some of the valuative analysis of singularities of plurisubharmonic (psh) functions developed by the first two authors. Following Kontsevich and Soibelman we describe the geometry of the space $\cV$ of all normalized valuations on $\C[x_1,\dots,x_n]$ centered at the origin. It is a union of simplices naturally endowed with an affine structure. Using relative positivity properties of divisors living on modifications of $\C^n$ above the origin, we define formal psh functions on $\cV$, designed to be analogues of the usual psh functions. For bounded formal psh functions on $\cV$, we define a mixed Monge-Ampère operator which reflects the intersection theory of divisors above the origin of $\C^n$. This operator associates to any $(n-1)$-tuple...

  8. Divisorial Valuations via Arcs

    de Fernex, Tommaso; Ein, Lawrence; Ishii, Shihoko
    This paper shows a finiteness property of a divisorial valuation in terms of arcs. First we show that every divisorial valuation over an algebraic variety corresponds to an irreducible closed subset of the arc space. Then we define the codimension for this subset and give a formula of the codimension in terms of ``relative Mather canonical class''. By using this subset, we prove that a divisorial valuation is determined by assigning the values of finite functions. We also have a criterion for a divisorial valuation to be a monomial valuation by assigning the values of finite functions.

  9. Flops Connect Minimal Models

    Kawamata, Yujiro
    A result by Birkar-Cascini-Hacon-McKernan together with the boundedness of length of extremal rays implies that different minimal models can be connected by a sequence of flops.

  10. The Orbibundle Miyaoka-Yau-Sakai Inequality and an Effective Bogomolov-McQuillanTheorem

    Miyaoka, Yoichi
    Let $X$ be a minimal projective surface of general type defined over the complex numbers and let $C \subset X$ be an irreducible curve of geometric genus $g$. Given a rational number $\alpha \in [0,1]$, we construct an orbibundle $\tilde{\mathcal{E}}_{\alpha}$ associated with the pair $(X,C)$ and establish the Miyaoka-Yau-Sakai inequality for $\tilde{\mathcal{E}}_{\alpha}$. By varying the parameter $\alpha$ in the inequality, we derive several geometric consequences involving the ``canonical degree'' $CK_X$ of $C$. Specifically we prove the following two results. (1) If $K_X^2$ is greater than the topological Euler number $c_2(X)$, then $CK_X$ is uniformly bounded from above by a function of the invariants $g, K_X^2$ and $c_2(X)$ (an effective version...

  11. Rigidity of Log Morphisms

    Moriwaki, Atsushi
    In this paper, we give the rigidity theorem for a log morphism as an extension of a fixed scheme morphism.

  12. On $\QQ$-conic Bundles

    Mori, Shigefumi; Prokhorov, Yuri
    A $\mathbb Q$-conic bundle is a proper morphism from a threefold with only terminal singularities to a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. We study the structure of $\mathbb Q$-conic bundles near their singular fibers. One corollary to our main results is that the base surface of every $\mathbb Q$-conic bundle has only Du Val singularities of type A (a positive solution of a conjecture by Iskovskikh). We obtain the complete classification of $\mathbb Q$-conic bundles under the additional assumption that the singular fiber is irreducible and the base surface is singular.

  13. Flops and Poisson Deformations of Symplectic Varieties

    Namikawa, Yoshinori

  14. A $\phi_{1,3}$-Filtration of the Virasoro Minimal Series $M(p,p')$ with $1< p'/p< 2$

    Feigin, B.; Feigin, E.; Jimbo, M.; Miwa, T.; Takeyama, Y.
    The filtration of the Virasoro minimal series representations $M^{(p,p')}_{r,s}$ induced by the $(1,3)$-primary field $\phi_{1,3}(z)$ is studied. For $1< p'/p< 2$, a conjectural basis of $M^{(p,p')}_{r,s}$ compatible with the filtration is given by using monomial vectors in terms of the Fourier coefficients of $\phi_{1,3}(z)$. In support of this conjecture, we give two results. First, we establish the equality of the character of the conjectural basis vectors with the character of the whole representation space. Second, for the unitary series ($p'=p+1$), we establish for each $m$ the equality between the character of the degree $m$ monomial basis and the character of the degree $m$ component in the associated graded module ${\rm gr}(M^{(p,p+1)}_{r,s})$...

  15. Holonomy Groups of Stable Vector Bundles

    Balaji, V.; Kollár, János
    We define the notion of holonomy group for a stable vector bundle $F$ on a variety in terms of the Narasimhan–Seshadri unitary representation of its restriction to curves. ¶ Next we relate the holonomy group to the minimal structure group and to the decomposition of tensor powers of $F$. Finally we illustrate the principle that either the holonomy is large or there is a clear geometric reason why it should be small.

  16. Professor Heisuke Hironaka’s Contribution in Promoting Mathematical Sciences and Bringing up Talent in New Generations

    Oda, Tadao
    In addition to his great accomplishments in mathematical research itself, Professor Hironaka has been very active since 1980 in trying to promote mathematical sciences and to bring up young mathematical scientists. His accomplishments in these respects are considerable as explained below.

  17. On the Mathematical Work of Professor Heisuke Hironaka

    Lê, D?ng Tráng; Teissier, Bernard
    In this succinct and incomplete presentation of Hironaka's published work up to now, it seems convenient to use a covering according to a few main topics: families of spaces and equisingularity, birational and bimeromorphic geometry, finite determinacy and algebraicity problems, flatness and flattening, real analytic and subanalytic geometry. This order follows roughly the order of publication of the first paper in each topic. One common thread is the frequent use of blowing-ups to simplify the algebraic problems or the geometry. For example, in the theory of subanalytic spaces of $\Rr^n$, Hironaka inaugurated and systematically used this technique, in contrast with...

  18. On $Q$-conic Bundles, II

    Mori, Shigefumi; Prokhorov, Yuri

  19. On “M-Functions” Closely Related to the Distribution of L'/L-Values

    Ihara, Yasutaka

  20. Symmetric Crystals for $gl?$

    Enomoto, Naoya; Kashiwara, Masaki
    In the preceding paper, we formulated a conjecture on the relations between certain classes of irreducible representations of a?ne Hecke algebras of type B and symmetric crystals for $gl?$. In the present paper, we prove the existence of the symmetric crystal and the global basis for $gl?$.

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