New nefness criteria for canonical divisors under weighted blow-ups produce 79 families of minimal 3-folds of general type, infinite families with Kodaira dimension 2, and 16 families on or near the Noether lines.
Varieties of general type with doubly exponential asymptotics
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abstract
We construct smooth projective varieties of general type with the smallest known volume and others with the most known vanishing plurigenera in high dimensions. The optimal volume bound is expected to decay doubly exponentially with dimension, and our examples achieve this decay rate. We also consider the analogous questions for other types of varieties. For example, in every dimension we conjecture the terminal Fano variety of minimal volume, and the canonical Calabi-Yau variety of minimal volume. In each case, our examples exhibit doubly exponential behavior.
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Construction of minimal varieties from quasi-smooth weighted complete intersections
New nefness criteria for canonical divisors under weighted blow-ups produce 79 families of minimal 3-folds of general type, infinite families with Kodaira dimension 2, and 16 families on or near the Noether lines.