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Dec 15, 2014 at 23:18 comment added Ashwath Rabindranath Thank you! Is there a reference about this that you could suggest?
Dec 15, 2014 at 16:56 comment added Donu Arapura Yes, there is a topological characterization. One can use the so called the 1st characteristic variety (or jump locus) which is the set of rank one local systems with nontrivial $H^1$. This forms a variety and the positive irreducible components through $1$ are in bijection with pencils.
Dec 15, 2014 at 7:31 history edited Ashwath Rabindranath CC BY-SA 3.0
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Dec 15, 2014 at 7:22 history asked Ashwath Rabindranath CC BY-SA 3.0