Varieties of general type with doubly exponential asymptotics
Louis Esser, Burt Totaro, Chengxi Wang
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.
Topics & Concepts
MathematicsDimension (graph theory)Fano planeProjective varietyConjectureExponential growthVariety (cybernetics)Type (biology)Pure mathematicsExponential functionVolume (thermodynamics)Exponential decayUpper and lower boundsCombinatoricsMathematical analysisStatisticsQuantum mechanicsBiologyEcologyPhysicsGeometry and complex manifoldsAlgebraic Geometry and Number TheoryAdvanced Algebra and Geometry