The degree of irrationality irr(X) of a n-dimensional complex projective variety X is the least degree of a dominant rational map from X to the n-dimensional projective space Pn. It is a well-known fact that given a product Xx(Pm) or a n-dimensional variety Y dominating X, their degrees of irrationality may be smaller than the degree of irrationality of X. In this paper, we focus on smooth surfaces S in the 3-dimensional projective space ‚P3 of degree d>4, and we prove that irr(Sx(Pm))=irr(S) for any integer m>0, whereas irr(Y)

On irrationality of surfaces in P3

BASTIANELLI, Francesco
2017-01-01

Abstract

The degree of irrationality irr(X) of a n-dimensional complex projective variety X is the least degree of a dominant rational map from X to the n-dimensional projective space Pn. It is a well-known fact that given a product Xx(Pm) or a n-dimensional variety Y dominating X, their degrees of irrationality may be smaller than the degree of irrationality of X. In this paper, we focus on smooth surfaces S in the 3-dimensional projective space ‚P3 of degree d>4, and we prove that irr(Sx(Pm))=irr(S) for any integer m>0, whereas irr(Y)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/201779
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