Tangent cones to generalised theta divisors and generic injectivity of the theta map
Journal article, Peer reviewed
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Original versionHitching GH, Hoff M. Tangent cones to generalised theta divisors and generic injectivity of the theta map. Compositio Mathematica. 2017;153(12):2643-2657 http://doi.org/10.1112/S0010437X17007539
Let be a Petri general curve of genus and a general stable vector bundle of rank and slope over with . For , we show how the bundle can be recovered from the tangent cone to the generalised theta divisor at . We use this to give a constructive proof and a sharpening of Brivio and Verra’s theorem that the theta map is generically injective for large values of .