The characteristic rank of a vector bundle ξ over a finite connected CW-complex X is by definition the largest integer ${k, 0 leq k leq mathrm{dim}(X)}$ , such that every cohomology class ${x in H^{j}(X;mathbb{Z}_2), 0 leq j leq k}$ , is a polynomial in the Stiefel–...
In this paper we give a complete description of finite-rank vector bundles on any linear ind-Grassmannian, and prove that any vector bundle of rank 2 on a twisted ind-Grassmannian is trivial. Our work extends work by W. Barth, J. Donin, I. Penkov, E. Sato, A. Tyurin...
The paper studies a rank 2 vector bundle on P1 x P3. Similarly to the Horrocks - Mumford bundle on P4 this vector bundle encodes a lot of geometric information. It is defined via the Serre construction by an abelian surface in P1 x P3. The bundle is stable with respect to O(1,1)...
vectorbundle; (iii)eachsimplebundleE′hasrank1unlessXisisomorphicG(k;∞)forsomek:inthe lattercaseE′,twistedbyasuitablelinebundle,isisomorphictoasimplesubbundleof thetensoralgebraT·(S),SbeingthetautologicalbundleofrankkonG(k;∞); (iv)eachsimplebundleE(andthuseachvectorbundleoffiniterankonX)istrivial...
Define Rank modus. Rank modus synonyms, Rank modus pronunciation, Rank modus translation, English dictionary definition of Rank modus. an excessive and unreasonable modus. See Modus, 3. See also: Rank Webster's Revised Unabridged Dictionary, published 19
Define rank order. rank order synonyms, rank order pronunciation, rank order translation, English dictionary definition of rank order. Noun 1. rank order - an arrangement according to rank ordering, order - the act of putting things in a sequential arran
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc. rank on someone in.to attack someone verbally; to gossip about someone. (see alsorank.)Please stop ranking on my family! See also:on,rank,someone ...
. A vector bundle E over an aCM variety F of dimension n is called aCM if all the intermediate cohomology groups of E vanish, namely if Hi(F,E(th))=0 for 0<i<n and t∈Z. If F is just Pn, then a well-known theorem of Horrocks (see [30] and references therein) states that...
A proof of the previous proposition will be given in the next section. We will frequently use the following version of the Riemann-Roch theorem for vector bundles: Theorem 2.3. If E is a rank 2 vector bundle on a smooth hypersurface X ⊂ P4 of degree 5 with Chern classes ci(E) = ...
We extend the concept of the Segre invariant to vector bundles on a surface X . For X = ℙ 2 we determine what numbers can appear as the Segre invariant of a rank 2 vector bundle with given Chern classes. The irreducibility of strata with fixed Segre i