Exceptional Fano varieties with small minimal log discrepancy
Louis Esser, Jihao Liu, Chengxi Wang
TL;DR
This paper constructs exceptional Fano varieties with minimal log discrepancies that decay doubly exponentially with dimension, achieving the optimal value in dimension 2, advancing understanding in algebraic geometry.
Contribution
It introduces a method to construct exceptional Fano varieties with minimal log discrepancies that are the smallest known across all dimensions.
Findings
Minimal log discrepancies decay doubly exponentially with dimension
Constructed varieties are well-formed hypersurfaces in weighted projective space
Achieved optimal minimal log discrepancy in dimension 2
Abstract
We construct exceptional Fano varieties with the smallest known minimal log discrepancies in all dimensions. These varieties are well-formed hypersurfaces in weighted projective space. Their minimal log discrepancies decay doubly exponentially with dimension, and achieve the optimal value in dimension 2.
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Mathematical Dynamics and Fractals