Sheaf (mathematics)
Tracking submanifolds with sheaves

Another common example of sheaves can be constructed by considering a complex submanifold Y ↪ X {\displaystyle Y\hookrightarrow X}. There is an associated sheaf O Y {\displaystyle {\mathcal {O}}_{Y}} which takes an open subset U ⊆ X {\displaystyle U\subseteq X} and gives the ring of holomorphic functions on U ∩ Y {\displaystyle U\cap Y}. This kind of formalism was found to be extremely powerful and motivates a lot of homological algebra such as sheaf cohomology since an intersection theory can be built using these kinds of sheaves from the Serre intersection formula.
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