Geodesic
A Regular Threefold of General Type with $p_{g} = 0$ and $P_{2} = 6$
Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 3, pp. 607-621.

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The range of the bigenus $P_{2}$ is one of the unsolved problems concerning smooth complex projective regular threefolds of general type with $p_{g} = 0$: The examples in the literature have $P_{2} \le 5$. In the present paper we present a non-singular threefold with $p_{g} = q_{1} = q_{2} = 0$; $P_{2} = 6$; the bicanonical map is stably birational. 
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Ronconi, M. Cristina. A Regular Threefold of General Type with $p_{g} = 0$ and $P_{2} = 6$. Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 3, pp. 607-621. http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_3_a5/

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