ample line bundle (Q3081): Difference between revisions

@@ Property / subclass of @@
+line bundle
@@ Property / subclass of: line bundle / rank @@
+Normal rank
@@ Property / nLab ID @@
+ample sheaf
@@ Property / nLab ID: ample sheaf / rank @@
+Normal rank
@@ Property / defining formula @@
+ $\exists n\in \mathbb {Z} ^{+}\exists (j\colon X\hookrightarrow \mathbb {P} ^{N})\colon {\mathcal {L}}^{\otimes n}=j^{*}{\mathcal {O}}(1)$ 
\exists n \in\mathbb Z^+ \exists (j\colon X \hookrightarrow \mathbb P^N) \colon \mathcal L^{\otimes n} = j^*\mathcal O(1)
+Normal rank
@@ Property / studied in @@
+algebraic geometry
@@ Property / studied in: algebraic geometry / rank @@
+Normal rank
@@ Property / studied in @@
+sheaf theory
@@ Property / studied in: sheaf theory / rank @@
+Normal rank
@@ Property / Microsoft Academic ID @@
+40926966
@@ Property / Microsoft Academic ID: 40926966 / rank @@
+Normal rank
@@ Property / Freebase ID @@
+/m/036mv4
@@ Property / Freebase ID: /m/036mv4 / rank @@
+Normal rank
@@ Property / OpenAlex ID @@
+C40926966
@@ Property / OpenAlex ID: C40926966 / rank @@
+Normal rank
@@ Property / OpenAlex ID: C40926966 / reference @@
+stated in: OpenAlex
retrieved: 26 January 2022Timestamp +2022-01-26T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
reference URL: https://docs.openalex.org/download-snapshot/snapshot-data-format
-Timestamp
++2022-01-26T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / Encyclopedia of Mathematics article ID @@
+Ample_sheaf
@@ Property / Encyclopedia of Mathematics article ID: Ample_sheaf / rank @@
+Normal rank
@@ Property / in defining formula @@
+ ${\mathcal {L}}$ 
\mathcal L
@@ Property / in defining formula: ${\mathcal {L}}$ / rank @@
+Normal rank
@@ Property / in defining formula: ${\mathcal {L}}$ / qualifier @@
+symbol represents: ample line bundle
@@ Property / in defining formula @@
+ ${\mathcal {O}}(1)^{*}$ 
\mathcal O(1)^*
@@ Property / in defining formula: ${\mathcal {O}}(1)^{*}$ / rank @@
+Normal rank
@@ Property / in defining formula: ${\mathcal {O}}(1)^{*}$ / qualifier @@
+symbol represents: tautological bundle
@@ Property / in defining formula @@
+ $\mathbb {P} ^{N}$ 
\mathbb P^N
@@ Property / in defining formula: $\mathbb {P} ^{N}$ / rank @@
+Normal rank
@@ Property / in defining formula: $\mathbb {P} ^{N}$ / qualifier @@
+symbol represents: projective space
@@ Property / in defining formula @@
+ $\mathbb {Z} ^{+}$ 
\mathbb Z^+
@@ Property / in defining formula: $\mathbb {Z} ^{+}$ / rank @@
+Normal rank
@@ Property / in defining formula: $\mathbb {Z} ^{+}$ / qualifier @@
+symbol represents: set of positive integers
@@ Property / PlanetMath ID @@
+Ample
@@ Property / PlanetMath ID: Ample / rank @@
+Normal rank
@@ Property / Stack Exchange tag @@
+https://mathoverflow.net/tags/ample-bundles
+Normal rank

Latest revision as of 15:49, 29 July 2024

line bundle on a variety, whose positive tensor power's sections can be used to embed the variety into a projective space

ample sheaf
ample bundle
ample invertible sheaf

Language	Label	Description	Also known as
English	ample line bundle	line bundle on a variety, whose positive tensor power's sections can be used to embed the variety into a projective space	ample sheaf ample bundle ample invertible sheaf