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for Varieties of secants on the generic curve

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For a smooth projective curve, the cycles of e-secant k-planes are among
the most studied objects in classical enumerative geometry, and there are
well-known formulas due to Castelnuovo, Cayley and MacDonald concerning
them. Despite various attempts, surprisingly little is known about the
enumerative validity of such formulas. We completely clarify this problem
in the case of the generic curve C of given genus and determine precisely
under which conditions the cycle of e-secant k-planes is non-empty and we
compute its dimension.

Return to Varieties of secants on the generic curve.

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