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.

A characterization of the symmetric square of a curve

PIROLA, GIAN PIETRO
2012

Abstract

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11571/223684
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