# zero locus of a sheaf homomorphism

The title says it all.

I'm just starting to go through the existence-proof of the quot scheme (http://www.math.utah.edu/~bertram/courses/hilbert/ps/hilbert.ps). On page 7, almost at the bottm of the page a scheme is defined as the zero locus of a homomorphism of sheaves.

What exactly is the zero locus of a sheaf homomorphism?

Greetings

Dan

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I would guess it's the set of points $p$ on the base where the stalk of the morphism is the zero morphism. – Andrew Nov 14 '12 at 22:37