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
Famous quotes containing the words stable, bundles and/or varieties:
“And neigh like Boanerges—
Then—punctual as a Star
Stop—docile and omnipotent
At its own stable door—”
—Emily Dickinson (1830–1886)
“He bundles every forkful in its place,
And tags and numbers it for future reference,
So he can find and easily dislodge it
In the unloading. Silas does that well.
He takes it out in bunches like birds’ nests.”
—Robert Frost (1874–1963)
“Now there are varieties of gifts, but the same Spirit; and there are varieties of services, but the same Lord; and there are varieties of activities, but it is the same God who activates all of them in everyone.”
—Bible: New Testament, 1 Corinthians 12:4-6.