The Variety of Positive Superdivisors of a Supercurve (Supervortices)

Details The Variety of Positive Superdivisors of a Supercurve (Supervortices) The Variety of Positive Superdivisors of a Supercurve (Supervortices)

1993-03-29

arxiv.org/abs/alg-geom/9303007v1

Mathematics

Algebraic Geometry

18 pages, AMS-TeX-ppt 2.1

Scientific paper

The supersymmetric product of a supercurve is constructed with the aid of a theorem of algebraic invariants and the notion of positive relative superdivisor (supervortex) is introduced. A supercurve of positive superdivisors of degree 1 (supervortices of vortex number 1) of the original supercurve is constructed as its supercurve of conjugate fermions, as well as the supervariety of relative positive superdivisors of degre p (supervortices of vortex number p.) A universal superdivisor is defined and it is proved that every positive relative superdivisor can be obtained in a unique way as a pull-back of the universal superdivisor. The case of SUSY-curves is discussed.

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