Euler sequence

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the Euler sequence is a particular <a href="/facts/Exact_sequence/leUJnwJb">exact sequence</a> of <a href="/facts/Sheaf_(mathematics)/MM3hcRw4">sheaves</a> on n-dimensional <a href="/facts/Projective_space/7MSpA9cM">projective space</a> over a <a href="/facts/Ring_(mathematics)/JnCUXz63">ring</a>. It shows that the <a href="/facts/Sheaf_of_relative_differentials/1aPfygbf">sheaf of relative differentials</a> is <a href="/facts/Stably_isomorphic/dNCXyK71">stably isomorphic</a> to an 
 
 
 
 (
 n
 +
 1
 )
 
 
 {\displaystyle (n+1)}
 
-fold sum of the dual of the Serre <a href="/facts/Twisting_sheaf/Vc2CmshX">twisting sheaf</a>.
The Euler sequence generalizes to that of a <a href="/facts/Projective_bundle/W7jjGmlW">projective bundle</a> as well as a <a href="/facts/Grassmann_bundle/3lnU9FhS">Grassmann bundle</a> (see the latter article for this generalization.)

Euler sequence open-in-new

Euler sequence