Locally free moduleLocally finite type moduleUpper topologyExterior power of a moduleIn this article, first we obtain a number of new results on projective modules and on the upper topology of an ordinal number. Then it is shown that the rank map of a locally finite type projective module is...
If E is an aCM bundle on the aCM variety F of dimension at least 2, then the minimal number of generators of ⁎H⁎0(F,E) as a module over the graded coordinate ring of F is rk(E)deg(F) at most (e.g. see [5]). For the above reason we introduce the following definit...
Thus the currents form a module over the smooth forms. We say that a current in CsM of the form [Math Processing Error]γs1a1⋯srar∂¯1sr+1ar+1∧⋯∂¯1sr′ar′, where γ is a test form, is elementary. A current τ on X is pseudomeromorphic if locally it is a ...
An algebraic discussion of the “syzygy problem”, which asks over a regular local ring whether every nonfree jth syzygy module must have rank ⩾ j. The corresponding problem for a vector bundle E (not a sum of line bundles) on Pn is this: if Hi(E(m)) = 0 for all i = 1,2,...
Locally free moduleLocally finite type moduleUpper topologyExterior power of a moduleIn this article, first we obtain a number of new results on projective modules and on the upper topology of an ordinal number. Then it is shown that the rank map of a locally finite type projective module is...
The reason is the Toda bracket \langle \eta ,\textsf{h},\eta \rangle = \{6\nu ,-6\nu \} from [22, Proposition 4.1]. Lemma 3.4 Let F be a field of characteristic neither 2 nor 3. The action of \eta on the \textbf{K}^{\textsf{MW}}-module \pi _{2+(\star )}\textbf{...
A coherent sheaf is flat if and only if it is locally free. We mention flatness, rather then local freeness, since we will relate it with flatness of projective morphism. Rossi introduces this notion of blowing up at coherent module, with the universal flattening property, within the complex...
and by considering flabby sheaves i.e. sheaves with surjective restriction maps; this last condition is a sufficient condition in order to glue together (via multipullbacks) principal comodule algebras locally defined on the base space to a globally defined one. in the noncommutative affine case,...
The modules of principal parts P k ( E ) of a locally free sheaf 蔚 on a smooth scheme X is a sheaf of O X -bimodules which is locally free as left and right O X -module. We explicitly split the modules of principal parts P k ( O ( n )) on the projective line in arbitrary...
Note that multiplication with η on the KMW-module π1+( )1/ηπ1+( )1 is the zero homomorphism by construction, which simplifies the term appearing in Lemma A.3. Hence Ext1KMW (KM, π1−( −1)1/ηπ1−( )1) = {0, 6ν} does not depend on the base field F. The ...