Classifying pluricanonical pencils on algebraic threefolds
Abstract
Let X be a normal projective
3-fold of general type with at worst Q-factorial terminal singularities.
We study the following conjecture:
for any integer m > 2, |mKX| is composed with a
pencil if any only if Pm(X) = 2. We prove that the
conjecture is true either for irrational pencils or for m bigger. We also classify
pluricanonical pencils for small value of m. There are dozens of
supporting examples according to Fletcher and Reid.
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