The fibers of the Prym map

Details The fibers of the Prym map The fibers of the Prym map

1992-06-17

arxiv.org/abs/alg-geom/9206008v2

Mathematics

Algebraic Geometry

71 pages, LATEX, (This is a reformatted version. It should print better than its predecessor.)

Scientific paper

In this work we use the bigonal, trigonal and tetragonal constructions to describe the fibers of the Prym map P : R_{g} ---->A_{g-1} inthe cases when it is dominant, i.e. for g < 7. The most interesting cases are g = 5, where the fiber is a double cover of the Fano surface of lines on a cubic threefold, and g=6, where the map is generically finite (of degree 27) with Galois group WE_{6}, so that the general fiber has the structure of the 27 lines on a cubic surface. For g > 6, the map is known to be generically injective. The tetragonal construction gives many counterexamples to injectivity, and we conjecture that all noninjectivity is due to the tetragonal construction.

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