Abstract
Let X be a smooth projective curve defined over a field k . The existence of tautological line bundles on X × Pic X / k is obstructed by a Brauer class α ∈ Br ( Pic X / k ) . We show that α splits at the generic points of various naturally defined loci in Pic X / k —the theta divisor and the generalized theta divisors associated with degree 2 g − 2 , semi-stable rank 2 vector bundles on X . We study a rank 2 analogue of Franchetta's theorem, and give explicit constructions of degree 2 g − 2 , semi-stable rank 2 vector bundles on the generic genus g curve.
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