In algebraic geometry, a reflexive sheaf is a coherent sheaf that is isomorphic to its second dual (as a sheaf of modules) via the canonical map. The...

it is a fractional ideal sheaf (see below). Conversely, every rank one reflexive sheaf corresponds to a Weil divisor: The sheaf can be restricted to the...

Riemann–Roch theorem. Picard group Divisor (algebraic geometry) Reflexive sheaf Quot scheme Twisted sheaf Essentially finite vector bundle Bundle of principal parts...

{\mathcal {O}}_{X}(D)} is the sheaf corresponding to a Weil divisor D (on a normal scheme). It need not be locally free, only reflexive. 4.  If D is a Q {\displaystyle...

words, one uses the dualizing sheaf on the ambient Pn to construct the dualizing sheaf on X. coherent duality reflexive sheaf Gorenstein ring Dualizing module...

definition in terms of gerbe; see § 2.1.3 of (Lieblich 2007). Reflexive sheaf Torsion sheaf Căldăraru, Andrei (2002). "Derived categories of twisted sheaves...

left/right adjectives in the statement is not a mistake.) Prüfer domain reflexive sheaf Eklof, P. C.; Mekler, A. H. (2002). Almost Free Modules - Set-theoretic...

classical algebraic geometry. This was re-expressed, with the advent of sheaf theory, in a way that made an analogy with Poincaré duality more apparent...

problem in particular. Let p : X ′ → X {\displaystyle p:X'\to X} . Each sheaf F on X gives rise to a descent datum ( F ′ = p ∗ F , α : p 0 ∗ F ′ ≃ p 1...

for various nice non-smooth X, the sheaf Ω h n {\displaystyle \Omega _{h}^{n}} recovers objects such as reflexive differentials and torsion-free differentials...

the schema T : ◻ A → A {\displaystyle \Box A\to A} . T is valid in any reflexive frame ⟨ W , R ⟩ {\displaystyle \langle W,R\rangle } : if w ⊩ ◻ A {\displaystyle...

singular cohomology with C-coefficients (equivalently, sheaf cohomology of the constant sheaf C) Hi(X) ⊗ H2n−i(X) → C, where n is the (complex) dimension...

compatibility conditions on the overlaps. Such a structure is known as a sheaf. Let V ⊆ U {\displaystyle V\subseteq U} be open subsets of R n . {\displaystyle...

analytic coherent sheaf over ( X , ω ) {\displaystyle (X,\omega )} . Namely in the algebraic setting the rank and degree of a coherent sheaf are encoded in...

( x , y ) {\displaystyle {\underline {\operatorname {Hom} }}(x,y)} is a sheaf of sets with respect to the induced Grothendieck topology on C / U {\displaystyle...

/ mes – 'I' / 'we', tu / jūs – 'you (singular) / you (plural)' and a reflexive pronoun savęs is indefinite, it means any of the genders. The word kas...

]\in {\check {H}}^{k}({\mathcal {U}},{\underline {A}})} for some constant sheaf of abelian groups can be represented as a function σ : ∐ U i 1 ⋯ i k → A...

pencil is sometimes referred to as a axial-pencil or fan of planes or a sheaf of planes. For example, the meridians of the globe are defined by the pencil...

that U is monadic: U reflects isomorphisms and C has coequalizers of reflexive pairs (those with a common right inverse) and U preserves those coequalizers...

differential geometry (e.g., Helgason). In a way, the sheaf-theoretic construction (i.e., the language of sheaf of modules) is more natural and increasingly more...

measurement, e.g., zuu koens hya one classifier thatch or couch grass "一捆茅草, a sheaf of thatch" • 【bhiek，捆】: it is usually used with a bundle of objects that...

mereological theories commonly assume that everything is a part of itself (reflexivity), that a part of a part of a whole is itself a part of that whole (transitivity)...

of a simple module is a division ring. Shapiro Shapiro's lemma sheaf of modules sheaf of modules snake snake lemma socle The socle is the largest semisimple...

impersonal passive forms and the use of the auxiliary verb "to have" for the reflexive voice (both traits shared with German). Modern Venetian is not a close...

X\times X} that satisfies the interpretations of the conditions for reflexivity, symmetry and transitivity. Every kernel pair p 0 , p 1 : R → X {\displaystyle...

("booth, stall") > ˈbúd (genitive plural) ⟨ã~õ⟩ alternate regularly. ˈlãba ("sheaf") > ˈlõb (genitive plural) ⟨aj~ˈôj⟩ alternate regularly. ˈjajô ("egg") >...

has been developed, in particular Mikio Sato's algebraic analysis, using sheaf theory and several complex variables. This extends the range of symbolic...

projective snc pair ( X , D ) {\displaystyle (X,D)} and every invertible sheaf A ∈ P i c ( X ) {\displaystyle A\in \mathrm {Pic} (X)} with κ ( A ) > p...