We construct a nonsingular threefold X of general type as a desingularization of a double space of degree 10 in P^4, of which an affine equation is t^2+f_{10}(x,y,z)=0. X has the birational invariants q_1=q_2=p_g=P_2=P_3=0,P_4=1 and its m-canonical transformation \varphi_{|mK_X|}, where K_X is a canonical divisor on X, has fibers that are generically finite sets if and only if m \geq 16, and it is birational if and only if m=23 or m \geq 27.
Gaps in the birationality of pluricanonical transformations.
STAGNARO, EZIO
2004
Abstract
We construct a nonsingular threefold X of general type as a desingularization of a double space of degree 10 in P^4, of which an affine equation is t^2+f_{10}(x,y,z)=0. X has the birational invariants q_1=q_2=p_g=P_2=P_3=0,P_4=1 and its m-canonical transformation \varphi_{|mK_X|}, where K_X is a canonical divisor on X, has fibers that are generically finite sets if and only if m \geq 16, and it is birational if and only if m=23 or m \geq 27.File in questo prodotto:
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