By A. Robert
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Additional resources for Elliptic Curves: Notes from Postgraduate Lectures Given in Lausanne 1971/72
I): the J1l(E) of global holomorphic differentials on E. )) ~ a: • (the lattice of "integral" holomorphic differential forms) which can be identified with L ~ a: under the preceding isomorphism. ", Z because L has no torsion, acts freely on the contractible space a: with quotient precisely E : Hurewitz Theorem). This group can also be interpreted as space of Z-bilinear alternate integral forms on L. B· ~ 7l The space HI(E,~~) is the most interesting one. It can be computed by taking a covering of E with open discs U.
B· ~ 7l The space HI(E,~~) is the most interesting one. It can be computed by taking a covering of E with open discs U. in ([ (mod L), each U~ being sufficiently small to avoid pairs z, z+ 4J (w E L - (OJ). Since all the Uo( and their finite intersections U ~ ... r(U"•... ef') ). p ) CoC, (3) ~ : (d,P) In other words, (o(,p Soft ~s = -1 '1) ~ s~1 so(l so(~ = = se(t1" s(31 f ¢ of the open intersecting discs U« . e. nu, · (when this triple intersection uo(~y is non-empty). ~ defined on the non-empty .
These line bundles would be the ~-powers of the canonical one (cotangent bundle), so that a modular form of u(-J. 7) expresses the degree of their divisors. 7): By hypothesis, n. (f) zero nor pole when Im(z» > - co , so that f has no Rand R is large enough. Let DR be the intersection of the fundamental domain D with is to integrate f'lf on the boundary ~DR Im(z)~ R. The idea of DR. In case f has zeros or poles on the sides, f'lf will have simple poles on the sides, and the usual modification of the contour has to be made.
Elliptic Curves: Notes from Postgraduate Lectures Given in Lausanne 1971/72 by A. Robert
Categories: Algebraic Geometry