coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information. Coherent sheaves can be seen as a generalization of...
40 KB (6,934 words) - 00:04, 8 June 2025
Proj construction (redirect from Serre twist sheaf)
twisting sheaf on the Proj of a ring does. Let E {\displaystyle {\mathcal {E}}} be a quasi-coherent sheaf on a scheme X {\displaystyle X} . The sheaf of symmetric...
19 KB (3,582 words) - 05:35, 6 March 2025
especially in algebraic geometry and the theory of complex manifolds, coherent sheaf cohomology is a technique for producing functions with specified properties...
26 KB (4,664 words) - 11:28, 9 October 2024
Function of several complex variables (section Idéal de domaines indéterminés (The predecessor of the notion of the coherent (sheaf)))
notion of the coherent sheaf into algebraic geometry, that is, the notion of the coherent algebraic sheaf. The notion of coherent (coherent sheaf cohomology)...
124 KB (17,717 words) - 22:01, 1 July 2025
Ample line bundle (redirect from Ample sheaf)
bundle p : E → Y {\displaystyle p\colon E\to Y} (or more generally a coherent sheaf on Y {\displaystyle Y} ) has a pullback to X {\displaystyle X} , f ∗...
40 KB (6,874 words) - 12:55, 26 May 2025
In mathematics, a sheaf of O-modules or simply an O-module over a ringed space (X, O) is a sheaf F such that, for any open subset U of X, F(U) is an O(U)-module...
19 KB (3,480 words) - 00:01, 5 June 2025
sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking, sheaf cohomology...
36 KB (5,833 words) - 23:25, 7 March 2025
a coherent sheaf F on a Stein manifold X. They are significant both as applied to several complex variables, and in the general development of sheaf cohomology...
4 KB (409 words) - 20:41, 7 March 2024
Look up sheaf in Wiktionary, the free dictionary. In mathematics, a sheaf (pl.: sheaves) is a tool for systematically tracking data (such as sets, abelian...
69 KB (11,082 words) - 14:18, 29 June 2025
In algebraic geometry, the dualizing sheaf on a proper scheme X of dimension n over a field k is a coherent sheaf ω X {\displaystyle \omega _{X}} together...
7 KB (1,018 words) - 22:42, 28 June 2025
Scheme (mathematics) (section Coherent sheaves)
quasi-coherent sheaf on a scheme X means an OX-module that is the sheaf associated to a module on each affine open subset of X. Finally, a coherent sheaf (on...
44 KB (7,139 words) - 07:51, 25 June 2025
geometry, a branch of mathematics, Serre duality is a duality for the coherent sheaf cohomology of algebraic varieties, proved by Jean-Pierre Serre. The...
18 KB (3,295 words) - 01:37, 25 May 2025
Analytic space (section Coherent sheaves)
ν. An analytic space is coherent if its structure sheaf O {\displaystyle {\mathcal {O}}} is a coherent sheaf. A coherent sheaf of O {\displaystyle {\mathcal...
7 KB (1,032 words) - 07:02, 10 June 2025
y]/(xy) are Cohen–Macaulay, but is not. coherent sheaf A coherent sheaf on a Noetherian scheme X is a quasi-coherent sheaf that is finitely generated as OX-module...
82 KB (12,496 words) - 00:02, 12 April 2025
Perfect complex (redirect from Pseudo-coherent sheaf)
module spectrum. When the structure sheaf O X {\displaystyle {\mathcal {O}}_{X}} is not coherent, working with coherent sheaves has awkwardness (namely the...
5 KB (562 words) - 09:42, 19 June 2025
geometry, a quasi-coherent sheaf on an algebraic stack X {\displaystyle {\mathfrak {X}}} is a generalization of a quasi-coherent sheaf on a scheme. The...
5 KB (711 words) - 22:03, 28 June 2024
In mathematics, the stalk of a sheaf is a mathematical construction capturing the behaviour of a sheaf around a given point. Sheaves are defined on open...
10 KB (1,588 words) - 01:58, 8 March 2025
cohomology groups (for coherent sheaves) as the much finer complex topology. However, for constant sheaves such as the sheaf of integers this does not...
33 KB (5,016 words) - 23:02, 25 May 2025
In algebraic geometry, the Castelnuovo–Mumford regularity of a coherent sheaf F over projective space P n {\displaystyle \mathbf {P} ^{n}} is the smallest...
3 KB (483 words) - 02:27, 27 April 2023
section. A slope of a vector bundle (or, more generally, a torsion-free coherent sheaf) E with respect to H is a rational number defined as μ ( E ) := c 1...
14 KB (1,887 words) - 23:40, 22 June 2025
if X is a projective scheme over a Noetherian scheme S and if F is a coherent sheaf on X, then there is a scheme Quot F ( X ) {\displaystyle \operatorname...
12 KB (2,273 words) - 20:32, 20 June 2025
Cohomology (section Sheaf cohomology)
André–Quillen cohomology Bounded cohomology BRST cohomology Čech cohomology Coherent sheaf cohomology Crystalline cohomology Cyclic cohomology Deligne cohomology...
44 KB (7,049 words) - 20:46, 13 January 2025
{\displaystyle {\mathcal {O}}_{X}} is coherent. Another important statement is as follows: for any coherent sheaf F {\displaystyle {\mathcal {F}}} on an...
19 KB (2,782 words) - 13:49, 12 June 2025
individual D-modules (and not more general complexes thereof); a perverse sheaf is in general represented by a complex of sheaves. The concept of perverse...
19 KB (2,265 words) - 05:36, 25 June 2025
bundle gives way to that of a coherent sheaf. Informally, Nakayama's lemma says that one can still regard a coherent sheaf as coming from a vector bundle...
22 KB (3,604 words) - 05:48, 21 November 2024
is the quasi-coherent sheaf of ideals cutting out Z, then the direct image i ∗ {\displaystyle i_{*}} from the category of quasi-coherent sheaves over...
5 KB (933 words) - 13:12, 18 June 2025
Coherent sheaf Invertible sheaf Sheaf cohomology Coherent sheaf cohomology Hirzebruch–Riemann–Roch theorem Grothendieck–Riemann–Roch theorem Coherent...
7 KB (600 words) - 19:55, 10 January 2024
reflexive sheaf is a coherent sheaf that is isomorphic to its second dual (as a sheaf of modules) via the canonical map. The second dual of a coherent sheaf is...
3 KB (380 words) - 01:38, 14 March 2025
Stack (mathematics) (redirect from 2-sheaf)
In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Stacks are used to formalise some of...
34 KB (5,116 words) - 02:17, 24 June 2025