Boundedness of fibers for pluricanonical maps of varieties of general type
Abstract
We prove that the r-th pluricanonical maps of threefolds of general type have birationally bounded fibers if r≥slant 2. Similarly, we prove that the r-th pluricanonical maps of fourfolds of general type have birationally bounded fibers if r≥slant 4. We extend these results to higher dimensions in terms of constants arising naturally from the birational geometry of varieties of general type.
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