Nagoya Mathematical Journal

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Volume 212 - December 2013

Contents

Sharp estimates of the potential kernel for the harmonic oscillator with applications
Adam Nowak, Krzysztof Stempak
Published online by Cambridge University Press: 11 January 2016, pp. 1-17
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We prove qualitatively sharp estimates of the potential kernel for the harmonic oscillator. These bounds are then used to show that the Lp–Lq estimates of the associated potential operator obtained recently by Bongioanni and Torrea are in fact sharp.

Generators for modules of vector-valued Picard modular forms
Fabien Cléry, Gerard Van Der Geer
Published online by Cambridge University Press: 11 January 2016, pp. 19-57
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We construct generators for modules of vector-valued Picard modular forms on a unitary group of type (2, 1) over the Eisenstein integers. We also calculate eigenvalues of Hecke operators acting on cusp forms.

New estimates of Hilbert–Kunz multiplicities for local rings of fixed dimension
Ian M. Aberbach, Florian Enescu
Published online by Cambridge University Press: 11 January 2016, pp. 59-85
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We present results on the Watanabe–Yoshida conjecture for the Hilbert–Kunz multiplicity of a local ring of positive characteristic. By improving on a “volume estimate” giving a lower bound for Hilbert–Kunz multiplicity, we obtain the conjecture when the ring has either Hilbert–Samuel multiplicity less than or equal to 5 or dimension less than or equal to 6. For nonregular rings with fixed dimension, a new lower bound for the Hilbert–Kunz multiplicity is obtained.

A note on thick subcategories of stable derived categories
Henning Krause, Greg Stevenson
Published online by Cambridge University Press: 11 January 2016, pp. 87-96
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For an exact category having enough projective objects, we establish a bijection between thick subcategories containing the projective objects and thick subcategories of the stable derived category. Using this bijection, we classify thick subcategories of finitely generated modules over strict local complete intersections and produce generators for the category of coherent sheaves on a separated Noetherian scheme with an ample family of line bundles.

The structure of sally modules and Buchsbaumness of associated graded rings
Kazuho Ozeki
Published online by Cambridge University Press: 11 January 2016, pp. 97-138
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Let A be a Noetherian local ring with the maximal ideal m, and let I be an m-primary ideal in A. This paper examines the equality on Hilbert coefficients of I first presented by Elias and Valla, but without assuming that A is a Cohen–Macaulay local ring. That equality is related to the Buchsbaumness of the associated graded ring of I.

Divisor class groups and graded canonical modules of multisection rings
Kazuhiko Kurano
Published online by Cambridge University Press: 11 January 2016, pp. 139-157
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We describe the divisor class group and the graded canonical module of the multisection ring T (X;D1,…, Ds) for a normal projective variety X and Weil divisors D1,…, Ds on X under a mild condition. In the proof, we use the theory of Krull domain and the equivariant twisted inverse functor.

Triangulation of the map of a G-manifold to its orbit space
Mitsutaka Murayama, Masahiro Shiota
Published online by Cambridge University Press: 11 January 2016, pp. 159-195
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Let G be a Lie group, and let M be a smooth proper G-manifold. Let M/G denote the orbit space, and let π : M → M/G be the natural map. It is known that M/G is homeomorphic to a polyhedron. In the present paper we show that there exist a piecewise linear (PL) manifold P, a polyhedron L, and homeomorphisms τ : P → M and σ : M/G → L such that σ o π o τ is PL. This is an application of the theory of subanalytic sets and subanalytic maps of Shiota. If M and the G-action are, moreover, subanalytic, then we can choose τ and σ subanalytic and P and L unique up to PL homeomorphisms.