Generalized Koszul complexes and Hochschild (co-)homology of complete intersections.
Geometric genera for ample vector bundles with regular sections.
Let X be a smooth complex projective variety of dimension n ≥ 3. A notion of geometric genus pg(X,E) for ample vector bundles E of rank r < n on X admitting some regular sections is introduced. The following inequality holds: pg(X,E) ≥ hn-r,0(X). The question of characterizing equality is discussed and the answer is given for E decomposable of corank 2. Some conjectures suggested by the result are formulated.