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arXiv · 1610.03456

Tangent cones to generalised theta divisors and generic injectivity of the theta map

George H. Hitching·Michael Hoff
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Abstract

Let $C$ be a Petri general curve of genus $g$ and $E$ a general stable vector bundle of rank $r$ and slope $g-1$ over $C$ with $h^0 (C, E) = r+1$. For $g > (2r+2)(2r+1)$, we show how the bundle $E$ can be recovered from the tangent cone to the theta divisor $\Theta_E$ at ${\mathcal O}_C$. We use this to give a constructive proof and a sharpening of Brivio and Verra's theorem that the theta map $SU_C (r) -rightarrow |r \Theta|$ is generically injective for large values of $g$.

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George H. Hitching, Michael Hoff. 2016-10-11. Tangent cones to generalised theta divisors and generic injectivity of the theta map. https://doi.org/10.1112/s0010437x17007539

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