All issues
Volume 29 (2006)
- Issue 3 Pages 319-
- Issue 2 Pages 163-
- Issue 1 Pages 1-
Predecessor
Volume 29, Issue 3
Displaying 1-10 of 10 articles from this issue
- |<
- <
- 1
- >
- >|
-
Wolfgang Ebeling2006 Volume 29 Issue 3 Pages 319-336
Published: 2006
Released on J-STAGE: February 22, 2007
JOURNAL FREE ACCESSM. Kobayashi introduced a notion of duality of weight systems. We tone this notion slightly down to a notion called coupling. We show that coupling induces a relation between the reduced zeta functions of the monodromy operators of the corresponding singularities generalizing an observation of K. Saito concerning Arnold's strange duality. We show that the weight systems of the mirror symmetric pairs of M. Reid's list of 95 families of Gorenstein K3 surfaces in weighted projective 3-spaces are strongly coupled. This includes Arnold's strange duality where the corresponding weight systems are strongly dual in Kobayashi's original sense. We show that the same is true for the extension of Arnold's strange duality found by the author and C. T. C. Wall.View full abstractDownload PDF (156K) -
Shigetoshi Bando2006 Volume 29 Issue 3 Pages 337-345
Published: 2006
Released on J-STAGE: February 22, 2007
JOURNAL FREE ACCESSThis is a publication of an old preprint which extended Futaki character to an obstruction for Chern class forms to be harmonic. Although there were considerable developments on the subject, this paper is presented "as was".View full abstractDownload PDF (85K) -
Akito Futaki2006 Volume 29 Issue 3 Pages 346-369
Published: 2006
Released on J-STAGE: February 22, 2007
JOURNAL FREE ACCESSIn this paper we will perturb the scalar curvature of compact Kähler manifolds by incorporating it with higher Chern forms, and then show that the perturbed scalar curvature has many common properties with the unperturbed scalar curvature. In particular the perturbed scalar curvature becomes a moment map, with respect to a perturbed symplectic structure, on the space of all complex structures on a fixed symplectic manifold, which extends the results of Donaldson and Fujiki on the unperturbed case.View full abstractDownload PDF (188K) -
Yuuki Tadokoro2006 Volume 29 Issue 3 Pages 370-382
Published: 2006
Released on J-STAGE: February 22, 2007
JOURNAL FREE ACCESSWe give an explicit computation of the pointed harmonic volumes of hyperelliptic curves with Weierstrass base points, which are paraphrased into a combinatorial formula.View full abstractDownload PDF (181K) -
Tran Tuan Nam2006 Volume 29 Issue 3 Pages 383-390
Published: 2006
Released on J-STAGE: February 22, 2007
JOURNAL FREE ACCESSLet M be a semi-discrete linearly compact module over a commutative noetherian ring R and i a non-negative integer. We show that the set of co-associated primes of the local homology R-module HiI (M) is finite in either of the following cases: (i) The R-modules HjI (M) are finite for all j < i; (ii) I ⊆ Rad(AnnR (HjI (M))) for all j < i. By Matlis duality we extend some results for the finiteness of associated primes of local cohomology modules HIi (M).View full abstractDownload PDF (90K) -
S. Ponnusamy, S. K. Sahoo2006 Volume 29 Issue 3 Pages 391-405
Published: 2006
Released on J-STAGE: February 22, 2007
JOURNAL FREE ACCESSAn analytic function f (z) = z + a2z2 + ··· in the unit disk Δ = {z : |z| < 1} is said to be in $¥mathcal{U}$ (λ, μ) if $$ ¥left|f'(z)¥left(¥frac{z}{f(z)} ¥right)^ {¥mu +1}-1 ¥right| ¥le ¥lambda ¥quad (|z|<1) $$ for some λ ≥ 0 and μ > -1. For -1 ≤ α ≤ 1, we introduce a geometrically motivated $¥mathcal{S}$p (α)-class defined by $${¥mathcal S}_p(¥alpha) = ¥left ¥{f¥in {¥mathcal S}: ¥left |¥frac{zf'(z)}{f(z)} -1¥right |¥leq {¥rm Re} ¥frac{zf'(z)}{f(z)}-¥alpha, ¥quad z¥in ¥Delta ¥right ¥},$$ where ${¥mathcal S}$ represents the class of all normalized univalent functions in Δ. In this paper, the authors determine necessary and sufficient coefficient conditions for certain class of functions to be in $¥mathcal{S}$p(α). Also, radius properties are considered for $¥mathcal{S}$p (α)-class in the class $¥mathcal{S}$. In addition, we also find disks |z| < r : = r (λ, μ) for which $¥frac{1}{r}$ f (rz) ∈ $¥mathcal{U}$ (λ, μ) whenever f ∈ $¥mathcal{S}$. In addition to a number of new results, we also present several new sufficient conditions for f to be in the class $¥mathcal{U}$ (λ, μ).View full abstractDownload PDF (125K) -
Elisabetta Barletta, Sorin Dragomir2006 Volume 29 Issue 3 Pages 406-454
Published: 2006
Released on J-STAGE: February 22, 2007
JOURNAL FREE ACCESSWe build a variational theory of geodesics of the Tanaka-Webster connection ∇ on a strictly pseudoconvex CR manifold M. Given a contact form θ on M such that (M, θ ) has nonpositive pseudohermitian sectional curvature (kθ (σ) ≤ 0) we show that (M, θ) has no horizontally conjugate points. Moreover, if (M, θ) is a Sasakian manifold such that kθ (σ) ≥ k0 > 0 then we show that the distance between any two consecutive conjugate points on a lengthy geodesic of ∇ is at most π/(2 $¥sqrt{k_0}$). We obtain the first and second variation formulae for the Riemannian length of a curve in M and show that in general geodesics of ∇ admitting horizontally conjugate points do not realize the Riemannian distance.View full abstractDownload PDF (362K) -
Frank Morgan2006 Volume 29 Issue 3 Pages 455-461
Published: 2006
Released on J-STAGE: February 22, 2007
JOURNAL FREE ACCESSWe provide generalizations of theorems of Myers and others to Riemannian manifolds with density and provide a minor correction to Morgan [8].View full abstractDownload PDF (77K) -
Marianna Fornasiero2006 Volume 29 Issue 3 Pages 462-474
Published: 2006
Released on J-STAGE: February 22, 2007
JOURNAL FREE ACCESSIn [12] Ishida introduces a complex, denoted by $¥tilde {¥Omega}^{^.}_Y$, associated to a filtered semi-toroidal variety Y over Spec C and proves that it is quasi-isomorphic to the Du Bois complex $¥underline{¥underline{¥Omega}}^{^.}_Y$ ([5]). In this article we regard a filtered semi-toroidal variety Y as an ideally log smooth log scheme over Spec C, and we give an interpretation of the Ishida complex $¥tilde{¥Omega}^{^.}_Y$ in terms of logarithmic geometry. Therefore, given a log smooth log scheme X over Spec C, we use this logarithmic interpretation of the Ishida complex to construct the following distinguished triangle in the Du Bois derived category Ddiff (X): IMω.X → $¥tilde{¥Omega}^{^.}_X$ → $¥tilde{¥Omega}^{^.}_D$ → ·, where D = X – Xtriv (Xtriv being the trivial locus for the log structure M on X). Since the complex IMω.X calculates the De Rham cohomology with compact supports of the smooth analytic space $X_{triv}^{an}$ ([20, Corollary 1.6]), this triangle is useful to give an interpretation of H.DR,c(Xtriv/C) as the hyper-cohomology of the simple complex $¥underline{¥underline{s}}[¥underline{¥underline{¥Omega}}^{^.}_X ¥longrightarrow ¥underline{¥underline{¥Omega}}^{^.}_D]$.View full abstractDownload PDF (151K) -
Manabu Shirosaki2006 Volume 29 Issue 3 Pages 475-484
Published: 2006
Released on J-STAGE: February 22, 2007
JOURNAL FREE ACCESSWe give relations of two meromorphic functions sharing 0, 1, ∞ and a set CM.View full abstractDownload PDF (107K)
- |<
- <
- 1
- >
- >|