Pacific Journal of Mathematics

We study a strong openness property for singular Hermitian vector bundles (E, h) that are Griffiths-semipositive.

We prove Howe duality for an exceptional theta correspondence.To that end, we relate the K -types of corresponding representations by exploiting a pair of see-saw identities.

We prove two theorems concerning the test properties of the Frobenius endomorphism over commutative Noetherian local rings of prime characteristic p.Our first theorem generalizes a result of Funk and Marley on the vanishing of Ext and Tor modules, while our second theorem generalizes one of our previous results on maximal Cohen-Macaulay tensor products.In these earlier results, we replace e R wit…

Let S be a complex smooth projective surface with a genus two fibration, and Aut s (S) the group of symplectic automorphisms, fixing every holomorphic 2-forms (if any) on S. Based on the work of Jin-Xing Cai, we show that, if (O S ) 5, then |Aut s (S)| 2. Then we verify, under some conditions, that Aut s (S) acts trivially on the Albanese kernel CH 0 (S) alb of the 0-th Chow group, which is predi…

We use the Saloff-Coste Sobolev inequality and the Nash-Moser iteration method to study the local and global behaviors of positive solutions to the nonlinear elliptic equation p u + au q = 0 defined on a complete Riemannian manifold (M, g) with Ricci lower bound, where p > 1 is a constant and p u = div(|u| p-2 u) is the usual p-Laplace operator.Under certain assumptions on a, p and q, we derive s…

We explicitly compute the Rankin-Selberg type integral introduced by Piatetski-Shapiro over adeles for vector-valued Siegel cusp forms of squarefree levels 0 .N /.On the way, for particular test functions in the Bessel models of irreducible admissible representations, exact evaluations of the local zeta integrals are given.

Since the 1980s, it has been known that the smallest non-finitely based semigroups are of order six.Surprisingly, for involution semigroups, a nonfinitely based example of order five was recently discovered.In this article, it is confirmed that every involution semigroup of order four is finitely based.Since every involution semigroup of order three or less is already known to be finitely based, …

x C q 0 be the one-dimensional Schrdinger equation with a repulsive delta potential.We study the Cauchy problem for the nonlinear equation (

We prove a number of structure and isomorphism results concerning the noncommutative Natsume-Olsen spheres 2 n 1 deformed along a skewsymmetric matrix 2 .These include (a) the fact that two C -algebras of the form 3 Mn are isomorphic precisely in the obvious cases; (b) the fact that m and n are recoverable from the isomorphism class of C. 2 m 1 /M n ; (c) the PI character, PI degree and Azumaya l…

The combinatorics of i -boxes has recently been introduced by Kashiwara, Kim, Oh and Park in the study of cluster algebras arising from the representation theory of quantum affine algebras.In this article, we associate to each chain of i -boxes a signed word, which canonically determines a cluster seed, following Berenstein, Fomin and Zelevinsky.By bridging these two different languages, we are a…

Let E/ be an elliptic curve.We say that E has a near coincidence of levelWe classify near coincidences of prime power level and use this result to give a classification of values of n for which Gal((E[n])/) is a nilpotent group.Along the way we prove a Gauss-Wantzel analog for the elliptic curve E :Assuming that there are no non-CM rational points on the modular curves X + ns ( p) for primes p > …

The Bnard-Conway invariant of links in the 3-sphere is a Casson-Lin type invariant defined by counting irreducible SU.2/-representations of the link group with fixed meridional traces.For two-component links with linking number one, the invariant has been shown to equal a symmetrized multivariable link signature.We extend this result to all two-component links with nonzero linking number.A key in…

Mekler's construction is a powerful technique for building purely algebraic structures from combinatorial ones.Its power lies in the fact that it allows various model-theoretic tameness properties of the combinatorial structure to transfer to the algebraic one.In this paper, we push this ideology much further, describing a broad class of properties that transfer through Mekler's construction.This…

Given a complex manifold containing a relatively compact Z(q) domain, we give sufficient geometric conditions on the domain so that its L 2 -cohomology in degree ( p, q) (known to be finite-dimensional) vanishes.The condition consists in the existence of a smooth weight function in a neighborhood of the closure of the domain, where the complex Hessian of the weight has a prescribed number of eige…

For a two-dimensional convex body, the Kovner-Besicovitch measure of symmetry is defined as the volume ratio of the largest centrally symmetric body contained inside the body to the original body. A classical result states that the Kovner-Besicovitch measure is at least $2/3$ for every convex body and equals $2/3$ for triangles. Lassak showed that an alternative measure of symmetry, i.e., symmetr…

The combinatorial hierarchical hyperbolicity criterion is a very useful way of constructing new hierarchically hyperbolic spaces (HHSs). We show that, conversely, HHSs satisfying natural assumptions (satisfied, for example, by mapping class groups) admit a combinatorial HHS structure. This can be useful in constructions of new HHSs, and also our construction clarifies how to apply the combinatori…

We prove that alternating chainmail links are L-space links.The proof is inspired by corresponding proofs for double branched covers of alternating links.More generally, we show that flat augmented chainmail links are generalized L-space links.Some other properties of these links are also considered.

We construct stable geometric and spectral transfer factors for a general reductive group and develop some of their basic properties, assuming the refined local Langlands correspondence.Using our definition of stable geometric transfer factors, we show that the stable transfer conjecture for orbital integrals implies the stable transfer of characters and vice versa.The latter is also implied by l…

We prove that the homological and Balmer spectra in tensor-triangular geometry are functorial in certain definable functors, thereby providing an alternative perspective on functoriality in tensor-triangular geometry from the viewpoint of purity, and generalising current results in the literature.