Numerical Bounds of Canonical Varieties
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We study surfaces and threefolds whose canonical maps are birational (canonical surfaces and threefolds). In the case of canonical surfaces we prove that the known inequlity for its invariants is not sharp if the surface is irregular. In the case of canonical threefolds we give a new lower bound for the self-intersection of the canonical divisor, depending on the geometric genus and the irregularity of the threefold.