On the Variety of Special Linear Systems on a General Algebraic Curve
نویسندگان
چکیده
0. Introduction (a) Statement of the problem and of the main theorem; some references 233 (b) Corollaries of the main theorem 236 (c) Role of the Brill-Noether matrix 238 (d) Heuristic reasoning for the dimension count; the CastelnuovoSeveri-Kleiman conjecture 240 (e) Notations and terminology 242 1. Reduction of the dimension count to the conjecture (a) Heuristic discussion 244 (b) Geometry of Castelnuovo canonical curves 246 (c) Dimension count on Castelnuovo canonical curves 248 (d) Proof of the reduction theorem 249 2. Proof of the Castelnuovo-Severi-Kleiman conjecture (a) Heuristic discussion; the crucial examples 254 (b) Completion of the argument 259 3. Multiplicities of W, (a) Heuristic discussion 261 (b) Computation of an intersection number 263 (c) Solution to an enumerative problem on Castelnuovo canonical curves 266 (d) Determination of multiplicities for a general smooth curve 270
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