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Volume 168 - 2002

Contents

Research Article

  • A determinant formula for a class of rational solutions of Painlevé V equation
  • Tetsu Masuda, Yasuhiro Ohta, Kenji Kajiwara
  • Published online by Cambridge University Press: 22 January 2016, pp. 1-25
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    We give an explicit determinant formula for a class of rational solutions of the Painlevé V equation in terms of the universal characters.

  • Boundary behavior of the Bergman metric
  • Bo-Yong Chen
  • Published online by Cambridge University Press: 22 January 2016, pp. 27-40
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    Let Ω be a bounded pseudoconvex domain in Cn. We give sufficient conditions for the Bergman metric to go to infinity uniformly at some boundary point, which is stated by the existence of a Hölder continuous plurisubharmonic peak function at this point or the verification of property (P) (in the sense of Coman) which is characterized by the pluricomplex Green function.

  • On Gorenstein surfaces dominated by P2
  • R. V. Gurjar, C. R. Pradeep, D.-Q. Zhang
  • Published online by Cambridge University Press: 22 January 2016, pp. 41-63
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    In this paper we prove that a normal Gorenstein surface dominated by P2 is isomorphic to a quotient P2/G, where G is a finite group of automorphisms of P2 (except possibly for one surface ). We can completely classify all such quotients. Some natural conjectures when the surface is not Gorenstein are also stated.

  • Shellability of semigroup rings
  • Annetta Aramova, Jürgen Herzog, Takayuki Hibi
  • Published online by Cambridge University Press: 22 January 2016, pp. 65-84
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    The concepts of Λ-shellability of locally finite posets as well as of extendable sequentially Koszul algebras will be introduced. It will be proved that the divisor poset of a homogeneous semigroup ring is Λ-shellable if and only if the semigroup ring is extendable sequentially Koszul. Examples of extendable sequentially Koszul semigroup rings contain all monomial ASL’s (algebras with straightening laws) and all second squarefree Veronese subrings.

  • Monogenesis of the rings of integers in certain imaginary abelian fields
  • Syed Inayat Ali Shah, Toru Nakahara
  • Published online by Cambridge University Press: 22 January 2016, pp. 85-92
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    In this paper we consider a subfield K in a cyclotomic field km of conductor m such that [km: K] = 2 in the cases of m = lpn with a prime p, where l = 4 or p > l = 3. Then the theme is to know whether the ring of integers in K has a power basis or does not.

  • Numerical criteria for certain fiber spaces to be birationally trivial
  • Jin-Xing Cai
  • Published online by Cambridge University Press: 22 January 2016, pp. 93-103
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    Let f: X → B be a fiber space over a curve B whose general fiber F belongs to one of the following type: 1) F is of general type and satisfying some mild conditions, 2) F is with trivial canonical sheaf. In this note, a numerical characterization for f: X → B to be birationally trivial is given.

  • On the cohomological completeness of q-complete domains with corners
  • Kazuko Matsumoto
  • Published online by Cambridge University Press: 22 January 2016, pp. 105-112
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    We prove the vanishing and non-vanishing theorems for an intersection of a finite number of q-complete domains in a complex manifold of dimension n. When q does not divide n, it is stronger than the result naturally obtained by combining the approximation theorem of Diederich-Fornaess for q-convex functions with corners and the vanishing theorem of Andreotti-Grauert for q-complete domains. We also give an example which implies our result is best possible.

  • The moduli space of bilevel-6 abelian surfaces
  • G. K. Sankaran, J. G. Spandaw
  • Published online by Cambridge University Press: 22 January 2016, pp. 113-125
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    We show that the moduli space of abelian surfaces with polarisation of type (1,6) and a bilevel structure has positive Kodaira dimension and indeed pg ≥ 3. To do this we show that three of the Siegel cusp forms with character for the paramodular symplectic group constructed by Gritsenko and Nikulin are cusp forms without character for the modular group associated to this moduli problem. We then calculate the divisors of the corresponding differential forms, using information about the fixed loci of elements of the paramodular group previously obtained by Brasch.

  • Special rays in the Mori cone of a projective variety
  • Marco Andreatta, Gianluca Occhetta
  • Published online by Cambridge University Press: 22 January 2016, pp. 127-137
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    Let X be a smooth n-dimensional projective variety over an algebraically closed field k such that KX is not nef. We give a characterization of non nef extremal rays of X of maximal length (i.e of length n – 1); in the case of Char(k) = 0 we also characterize non nef rays of length n – 2.

  • Glauber dynamics for fermion point processes
  • Tomoyuki Shirai, Hyun Jae Yoo
  • Published online by Cambridge University Press: 22 January 2016, pp. 139-166
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    We construct a Glauber dynamics on {0, 1}ℛ, ℛ a discrete space, with infinite range flip rates, for which a fermion point process is reversible. We also discuss the ergodicity of the corresponding Markov process and the log-Sobolev inequality.

Front Matter

  • NMJ volume 168 Cover and Front matter
  • Published online by Cambridge University Press: 22 January 2016, pp. f1-f3
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