A characterization of the symmetric square of a curve

Details A characterization of the symmetric square of a curve A characterization of the symmetric square of a curve

2010-08-10

arxiv.org/abs/1008.1790v1

Mathematics

Algebraic Geometry

International Mathematics Research Notices 2011

Scientific paper

10.1093/imrn/rnr025

In this paper a new intrinsic geometric characterization of the symmetric square of a curve and of the ordinary product of two curves is given. More precisely it is shown that the existence on a surface of general type S of irregularity q of an effective divisor D having self-intersection D^2>0 and arithmetic genus q implies that S is either birational to a product of curves or to the second symmetric product of a curve.

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