International Mathematics Research Notices

doi: 10.1093/imrn/rnt306pmid: N/A

doi: 10.1093/imrn/rnt330pmid: N/A

doi: 10.1093/imrn/rnt282pmid: N/A

Ma, Linquan

doi: 10.1093/imrn/rnt130pmid: N/A

In this paper, we show that for an F-pure local ring , all local cohomology modules have finitely many Frobenius compatible submodules. This answers positively the open question raised by Enescu and Hochster [3] (see also [2], where it was stated as a conjecture when R is CohenMacaulay). We also prove that when is excellent and F-pure on the punctured spectrum, all local cohomology modules have finite length in the category of R-modules with Frobenius action. Finally, we show that the property that all have finitely many Frobenius compatible submodules passes to localizations.

Boyer, Charles P.; Tnnesen-Friedman, Christina W.

doi: 10.1093/imrn/rnt139pmid: N/A

In this paper, we study the Sasakian geometry on S3-bundles over a Riemann surface g of genus g>0 with an emphasis on extremal Sasaki metrics. We prove the existence of a countably infinite number of inequivalent contact structures on the total space of such bundles that admit 2D Sasaki cones each with a Sasaki metric of constant scalar curvature (CSC). This CSC Sasaki metric is most often irregular. We further study the extremal subset in the Sasaki cone showing that if 0<g4 it exhausts the entire cone. Examples are given where exhaustion fails.

Indrei, Emanuel; Marcon, Diego

doi: 10.1093/imrn/rnt138pmid: N/A

We prove a sharp, dimension-free stability result for the classical logarithmic Sobolev inequality for a two parameter family of functions. Roughly speaking, our family consists of a certain class of log C1,1 functions. Moreover, we show how to enlarge this space at the expense of the dimensionless constant and the sharp exponent. As an application, we obtain new bounds on the entropy.

Eaton, Charles W.; Moret, Alexander

doi: 10.1093/imrn/rnt131pmid: N/A

We propose a generalization of Brauer's Height Zero Conjecture that considers positive heights. We give strong evidence supporting one half of the generalization and obtain some partial results regarding the other half.

Medori, Costantino; Spiro, Andrea

doi: 10.1093/imrn/rnt129pmid: N/A

Let M be a CR manifold of hypersurface type, which is Levi degenerate but also satisfying a k-nondegeneracy condition at all points. This might be only if and if , then k2 at all points. We prove that for any five-dimensional, uniformly two-nondegenerate CR manifold M there exists a canonical Cartan connection, modeled on a suitable projective completion of the tube over the future light cone . This determines a complete solution to the equivalence problem for this class of CR manifolds.

Draisma, Jan; Rodriguez, Jose

doi: 10.1093/imrn/rnt128pmid: N/A

In a recent paper, Hauenstein, Sturmfels, and the second author discovered a conjectural bijection between critical points of the likelihood function on the complex variety of matrices of rank r and critical points on the complex variety of matrices of co-rank r1. In this paper, we prove that conjecture for rectangular matrices and for symmetric matrices, as well as a variant for skew-symmetric matrices.

Pushnitski, Alexander; Volberg, Alexander

doi: 10.1093/imrn/rnt137pmid: N/A

We give a new sufficient condition for existence and completeness of wave operators in an abstract scattering theory. This condition generalizes both trace class and smooth approaches to the scattering theory. Our construction is based on estimates for the Cauchy transforms of operator-valued measures.