Arc valuations on smooth varieties
JOURNAL OF ALGEBRA
Authors: More, Yogesh
Abstract
Let X be a nonsingular variety (with dim X >= 2) over an algebraically closed field k of characteristic zero. Let alpha :Spec k[t] -> X be an arc on X, and let v = ord(alpha) be the valuation given by the order of vanishing along alpha. We describe the maximal irreducible subset C(v) of the arc space of X such that val(C(v)) = v. We describe C(v) both algebraically, in terms of the sequence of valuation ideals of v, and geometrically, in terms of the sequence of infinitely near points associated to v. As a corollary, we get that v is determined by its sequence of centers. Also, when X is a surface, our construction also applies to any divisorial valuation v, and in this case C(v) coincides with the one introduced in [L Ein, R. Lazars-feld, M. Mustata, Contact loci in arc spaces, Compos. Math. 140 (2004) 1229-1244, Example 2.5]. (C) 2009 Elsevier Inc. All rights reserved.
Mutations of alpha spectrin and labial block cuprophilic cell differentiation and acid secretion in the middle midgut of Drosophila larvae
DEVELOPMENTAL BIOLOGY
Authors: Dubreuil, RR; Frankel, J; Wang, P; Howrylak, J; Kappil, M; Grushko, TA
Abstract
Mutations in Drosophila alpha spectrin cause larval lethality and defects in cell shape and adhesion (J. Lee et al., 1993, J. Cell Biol. 123, 1797-1809). Here we examined the effects of two lethal alpha spectrin alleles (alpha-spec(rg41) and alpha.spec(rg35)) on development and function of the larval midgut. Homozygous null alpha-spec(rg41)-mutant larvae exhibited a striking defect in middle midgut acidification. In contrast, many homozygous alpha.spec(rg35) mutants were capable of acidification, indicating partial function of the truncated alpha-spec(rg35) product. Acidification was also blocked by a mutation in the labial gene, which is required for differentiation of cuprophilic cells in the midgut, suggesting that these cells secrete acid. We found that two isoforms of spectrin (alpha beta and alpha beta(H)) are segregated within the basolateral and apical domains of cuprophilic cells, respectively. The most conspicuous defect in cuprophilic cells from labial and alpha spectrin mutants was in morphogenesis of the invaginated apical domain, although basolateral defects may also contribute to the acidification phenotype. Acid secretion in vertebrate systems is thought to involve the polarized activities of apical proton pumps and basolateral anion exchangers, both of which interact with spectrin. We propose that the alpha-spe(rg41) mutation in Drosophila interferes with the polarized activities of homologous molecules that drive acid secretion in cuprophilic cells. (C) 1998 Academic Press.