Let X be a smooth complex projective variety such that the Albanese map of X is generically finite onto its image. Here we study the so-called eventual m-paracanonical map of X, whose existence is implied by the results of [4] (when m = 1 we also assume χ(KX ) > 0). We show that for m = 1 this map behaves in a similar way to the canonical map of a surface of general type, as described in [6], while it is birational for m > 1. We also describe it explicitly in several examples.
The eventual paracanonical map of a variety of maximal Albanese dimension
Pardini R.;Stoppino L.
2019-01-01
Abstract
Let X be a smooth complex projective variety such that the Albanese map of X is generically finite onto its image. Here we study the so-called eventual m-paracanonical map of X, whose existence is implied by the results of [4] (when m = 1 we also assume χ(KX ) > 0). We show that for m = 1 this map behaves in a similar way to the canonical map of a surface of general type, as described in [6], while it is birational for m > 1. We also describe it explicitly in several examples.File in questo prodotto:
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