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A Threefold of General Type with q 1=q 2=p g =P 2=0

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Abstract

One of the problems in classifying nonsingular threefolds of general type with p g =0 lies in finding the range of the bigenus P 2 (surfaces of general type with p g =0 have 2≤P 2≤10). Another problem involves finding the minimum integer m such that the m-canonical map Φ|mK| is birational for any threefold (m=5 in the case of surfaces). An example of a nonsingular threefold X of general type with q 1=q 2=0, p g =P 2=0,P 3=1 is presented. In addition, the m-canonical map of X is birational if and only if m≥14. The threefold is obtained as a nonsingular model of a degree ten hypersurface in P 4 C with the affine equation t 2=f 10(x,y,z).

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  1. Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Padova, Via Belzoni 7, 35131, Padova, Italy

    M. Cristina Ronconi

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  1. M. Cristina Ronconi
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Ronconi, M.C. A Threefold of General Type with q 1=q 2=p g =P 2=0. Acta Applicandae Mathematicae 75, 133–150 (2003). https://doi.org/10.1023/A:1022336011727

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