Abstract
We describe the osculating cone to Brill–Noether loci $$W^0_d(C)$$ at smooth isolated points of $$W^1_d(C)$$ for a general canonically embedded curve C of even genus $$g=2(d-1)$$ . In particular, we show that the canonical curve C is a component of the osculating cone. The proof is based on techniques introduced by George Kempf.
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