Bounds on cohomology and Castelnuovo-Mumford regularity

The Castelnuovo-Mumford regularity reg(X) of a projective scheme X was introduced by Mumford by generalizing ideas of Castelnuovo. The interest in this concept stems partly from the fact that X is m-regular if and only if for every p \geq 0 the minimal generators of the p-th syzygy module of the defining ideal I of X occur in degree \leq m + p. There are some bounds in the case that X is a locally Cohen-Macaulay scheme. The aim of this paper is to extend and improve these results for so-called (k,r)-Buchsbaum schemes. In order to prove our theorems, we need to apply a spectral sequence. We conclude by describing two sharp examples and open problems.Comment: LaTeX, 18 page

Towards a theory of arithmetic degrees

The aim of this paper is to start a systematic investigation of the arithmetic degree of projective schemes as introduced by D. Bayer and D. Mumford. One main theme concerns itself with the behaviour of this arithmetic degree under hypersurface sections. The notion of arithmetic degree involves the new concept of length-multiplicity of embedded primary ideals. Therefore it is much harder to control the arithmetic degree under a hypersurface section than in the case for the classical degree theory. Nevertheless it has important and interesting applications. We describe such applications to the Castelnuovo-Mumford regularity and to Bezout-type theorems.Comment: LaTeX, 14 page

Bounds on Castelnuovo-Mumford regularity for divisors on rational normal scrolls

The Castelnuovo-Mumford regularity is one of the most important invariants in studying the minimal free resolution of the defining ideals of the projective varieties. There are some bounds on the Castelnuovo-Mumford regularity of the projective variety in terms of the other basic invariants such as dimension, codimension and degree. This paper studies a bound on the regularity conjectured by Hoa, and shows this bound and extremal examples in the case of divisors on rational normal scrolls

The tertiary structure of the human Xkr8–Basigin complex that scrambles phospholipids at plasma membranes

Xkr8–Basigin is a plasma membrane phospholipid scramblase activated by kinases or caspases. We combined cryo-EM and X-ray crystallography to investigate its structure at an overall resolution of 3.8 Å. Its membrane-spanning region carrying 22 charged amino acids adopts a cuboid-like structure stabilized by salt bridges between hydrophilic residues in transmembrane helices. Phosphatidylcholine binding was observed in a hydrophobic cleft on the surface exposed to the outer leaflet of the plasma membrane. Six charged residues placed from top to bottom inside the molecule were essential for scrambling phospholipids in inward and outward directions, apparently providing a pathway for their translocation. A tryptophan residue was present between the head group of phosphatidylcholine and the extracellular end of the path. Its mutation to alanine made the Xkr8–Basigin complex constitutively active, indicating that it plays a vital role in regulating its scramblase activity. The structure of Xkr8–Basigin provides insights into the molecular mechanisms underlying phospholipid scrambling

Yeast functional assay of the p53 gene status in human cell lines maintained in our laboratory

We used a yeast functional assay (functional analysis of separated alleles in yeast: FASAY) to determine the p53 gene status of human cell lines maintained in our laboratory. This assay enables the researcher to score wild-type p53 expression on the basis of the ability of expressed p53 to transactivate the reporter gene HIS 3 via the p53-responsive GAL 1 promoter in Saccharomyces cerevisiae. The cell lines examined were ten hepatoma, two hepatoblastoma, three in vitro immortalized fibroblast, two osteosarcoma, a chondrosarcoma, an ovarian teratocarcinoma and a colon cancer cell line. Out of 20 cell lines, 11 cell lines had mutations in both alleles of the p53 gene, and another 8 cell lines had no mutation in the p53 gene. Thus, 55% of the cell lines examined had mutations in the p53. Interestingly, PA-1 cells had both the normal and the mutant p53 alleles, showing that FASAY is a useful method for detecting the wild-type and mutated p53 genes simultaneously. As for the three liver cell lines harboring HBsAg, there was no relationship between their p53 gene status and the presence of HBsAg. Two cell lines were normal for p53 status, while the other had a mutation of the p53 gene.</p

Sharp bounds on Castelnuovo-Mumford regularity

The Castelnuovo-Mumford regularity is one of the most important invariants in studying the minimal free resolution of the defining ideals of the projective varieties. There are some bounds on the Castelnuovo-Mumford regularity of the projective variety in terms of the other basic measures such as dimension, codimension and degree. In this paper we consider an upper bound on the regularity reg(X) of a nondegenerate projective variety X, reg(X)≤⎾(deg(X)-1)/codim(X)⏋+k・dim(X), provided X is k-Buchsbaum for k≥1, and investigate the projective variety with its Castelnuovo-Mumford regularity having such upper bound

Remarks on r-planes in Complete Intersections

This paper investigates the families of smooth complete intersections containing r-planes in projective spaces. We are going in a primitive way to shed some light on a point and an r-plane containing the point in a complete intersection from the viewpoint of projective geometry

Bounds on Castelnuovo-Mumford Regularity for Divisors on Rational Normal Scrolls

The Castelnuovo-Mumford regularity is one of the most important invariants in studying the minimal free resolution of the defining ideas of the projective varieties. There are some bounds on the Castelnuovo-Mumford regularity of the projective variety in terms of the other basic invariants such as dimension, codimension and degree. This paper studies a bound on the regularity conjectured by Hoa, and shows this bound and extremal examples in the case of divisors on rational normal scrolls