On the Geometry of a Theorem of Riemann
1973; Princeton University; Volume: 98; Issue: 1 Linguagem: Inglês
10.2307/1970910
ISSN1939-8980
Autores Tópico(s)Advanced Algebra and Geometry
ResumoLet C be a smooth complete algebraic curve. Let I: C-+J be an universal abelian integral of C into its Jacobian J. Furthermore, let I(i): C(i) J be the mapping sending a point c1 + *-+ ci in the ith symmetric product C(i) to I(c1) + *-+ I(ci). Let Wi be the image of I(i) when i is less than the dimension of J. My purpose is to describe the tangent cone of Wi at any point. Let L(w) be the inverse image by I(i) of a point w in J. L(w) is a projective space representing a complete linear system of effective divisors on C. Geometrically, my main result is
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