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In mathematics, the Euler sequence is a particular exact sequence of sheaves on n-dimensional projective space over a ring. It shows that the sheaf of relative differentials is stably isomorphic to an -fold sum of the dual of the Serre twisting sheaf. The Euler sequence generalizes to that of a projective bundle as well as a Grassmann bundle (see the latter article for this generalization.)

Attributes	Values
rdfs:label	Euler sequence (en) Точная последовательность Эйлера (ru) Eulers följd (sv) 欧拉正合列 (zh)
rdfs:comment	In mathematics, the Euler sequence is a particular exact sequence of sheaves on n-dimensional projective space over a ring. It shows that the sheaf of relative differentials is stably isomorphic to an -fold sum of the dual of the Serre twisting sheaf. The Euler sequence generalizes to that of a projective bundle as well as a Grassmann bundle (see the latter article for this generalization.) (en) Точная последовательность Эйлера — это определённая точная последовательность пучков на n-мерном проективном пространстве над кольцом. Она показывает, что кокасательное расслоение проективного пространства (n + 1)-кратной сумме тавтологических расслоений (см. скручивающий пучок Серра). (ru) Inom matematiken är Eulers följd en viss exakt följd av kärven på n-dimensionella över en ring. Den bevisar att kärven av relativa differentialer är stabilt isomorfisk till en (n + 1)-faldig summa av dualen av Serres böjda kärve. (sv) 在代数几何学中，欧拉正合列是环上的射影空间层构成的一个正合列。欧拉正合列实质上说明了层稳定同构于塞尔的对偶的n重和。欧拉正合列可以被推广到或者格拉斯曼丛上的情形。 (zh)
dcterms:subject	Projective geometry Algebraic geometry
Wikipage page ID	21166036 (xsd:integer)
Wikipage revision ID	1093533463 (xsd:integer)
Link from a Wikipage to another Wikipage	Projective space Projective bundle De Gruyter Algebraic geometry of projective spaces Vector field Vector space Mathematics Geometric genus Chow group Fano varieties Ample line bundle Projective geometry Exterior power Field (mathematics) Grassmann bundle Ring (mathematics) Algebraic geometry Chern class Stably isomorphic Sheaf (mathematics) Exact sequence Canonical sheaf Twisting sheaf Tangent sheaf Sheaf of relative differentials dbr:Euler_vector_field
sameAs	Euler sequence Euler sequence Euler sequence Euler sequence Euler sequence Euler sequence
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Hartshorne_AG
has abstract	In mathematics, the Euler sequence is a particular exact sequence of sheaves on n-dimensional projective space over a ring. It shows that the sheaf of relative differentials is stably isomorphic to an -fold sum of the dual of the Serre twisting sheaf. The Euler sequence generalizes to that of a projective bundle as well as a Grassmann bundle (see the latter article for this generalization.) (en) Точная последовательность Эйлера — это определённая точная последовательность пучков на n-мерном проективном пространстве над кольцом. Она показывает, что кокасательное расслоение проективного пространства (n + 1)-кратной сумме тавтологических расслоений (см. скручивающий пучок Серра). (ru) Inom matematiken är Eulers följd en viss exakt följd av kärven på n-dimensionella över en ring. Den bevisar att kärven av relativa differentialer är stabilt isomorfisk till en (n + 1)-faldig summa av dualen av Serres böjda kärve. (sv) 在代数几何学中，欧拉正合列是环上的射影空间层构成的一个正合列。欧拉正合列实质上说明了层稳定同构于塞尔的对偶的n重和。欧拉正合列可以被推广到或者格拉斯曼丛上的情形。 (zh)
gold:hypernym	Sequence
prov:wasDerivedFrom	wikipedia-en:Euler_sequence?oldid=1093533463&ns=0
page length (characters) of wiki page	6886 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Euler_sequence
is Link from a Wikipage to another Wikipage of	Euler exact sequence Algebraic geometry of projective spaces List of things named after Leonhard Euler Derived noncommutative algebraic geometry Glossary of algebraic geometry Convexity (algebraic geometry) Stable vector bundle Complex projective space Grassmann bundle Birkhoff–Grothendieck theorem Coherent sheaf Tautological bundle Picard group Residual intersection
is Wikipage redirect of	Euler exact sequence
is foaf:primaryTopic of	wikipedia-en:Euler_sequence

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