Stable Vector Bundles Over Projective Varieties
If X is a smooth projective variety of dimension n and H is a hyperplane section, then a vector bundle (or torsionfree sheaf) W is called stable if
for all proper non-zero subbundles (or subsheaves) V of W, where denotes the Euler characteristic of an algebraic vector bundle and the vector bundle means the n-th twist of V by H. W is called semistable if the above holds with < replaced by ≤.
There are also other variants in the literature: cf. this thesis p.29.
Read more about this topic: Stable Vector Bundle
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