TL;DR
This paper classifies all toric Fano threefolds with canonical singularities, identifying a total of 674,688 varieties using an inductive approach, thereby advancing the understanding of their structure and classification.
Contribution
It introduces an inductive method for classifying toric Fano varieties and provides a complete classification of those with canonical singularities in three dimensions.
Findings
Identified 674,688 toric Fano threefolds with canonical singularities.
Developed an inductive classification technique for toric Fano varieties.
Established a comprehensive list of such varieties up to isomorphism.
Abstract
An inductive approach to classifying toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are 674,688 such varieties.
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