Bogomolov’s Inequality and Applications
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Our main goal in this chapter will be to give a proof of the following: Theorem 1 (Bogomolov). Let X be an algebraic surface and let H be an ample divisor on X. Suppose that V is an H-stable rank 2 vector bundle on X. Then c 1 2 (V) ≤ 4c2(V). Equivalently, p1(ad V) ≤ 0.
KeywordsExact Sequence Vector Bundle Line Bundle Galois Group Coherent Sheaf
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