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Vanishings for the cohomology of certain families of stable rank two vector bundles on \(\mathbb{P}^ 3\). (English) Zbl 0889.14007

The author obtains explicit descriptions of two families of rank 2 stable vector bundles on \(\mathbb{P}^3\). The first has \(c_1=0\), \(c_2=2m+2\) and spectrum \((-m,-m+1, \dots, 1,0^2,1, \dots, m)\) and the second \(c_1 =-1\), \(c_2= 2m-2\) \((m\geq 2)\) and spectrum \((-m+1, \dots, m-2)\). From these descriptions the author obtains vanishing theorems for the first cohomology groups. He also obtains further results for \(c_1=-1\), \(\text{sp}= (-1^a, 0^a)\) and also for \(-1\leq c_1 \leq 0\), \(c_2\leq 6\). These results confirm conjectures of M.-C. Chang [Math. Ann. 262, 511-516 (1983; Zbl 0505.14013)].

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14F17 Vanishing theorems in algebraic geometry
57R20 Characteristic classes and numbers in differential topology

Citations:

Zbl 0505.14013
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References:

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