IJPAM: Volume 66, No. 3 (2011)

EXAMPLES OF THREEFOLDS WITH
$q_1=q_2=p_g=0$ AND $ 3\leq P_2 \leq 4$

Remo Gattazzo
Department of Methods and Mathematical Models of Applied Sciences
University of Padua
63, Via Trieste, Padua, 35121, ITALY
e-mail: remo.gattazzo@unipd.it


Abstract.Threefolds of general type with $q_1=q_2=p_g=0$ and $P_2=0,1,2,5,6$ are been found as desingularization of sextic hypersurfaces of $\Pf^4$. We give two examples $X_i, (i=1,2)$ having $P_2=3,4$. They are different from other examples with $p_g=0$ present in the literature constructed as weighted complete intersections because they have different $P_3$ and $P_4$. We study the pluricanonical maps $\varphi_{\vert mK_{X_i}\vert}$ and show that $X_i, i=1,2,$ are birational for $m\ge 4.$

Received: December 3, 2010

AMS Subject Classification: 14E05, 14J30

Key Words and Phrases: threefolds, pluricanonical maps

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 3