Abstract
In this paper, an update on the classification of smooth weak Fano threefolds with Picard number two and small anti-canonical maps is given. Geometric constructions are provided for previously open numerical cases by blowing up certain curves on smooth Fano threefolds of Picard number one. This paper provides updated tables in the last section and reduces the 14 remaining E1-E* open cases to four.
Acknowledgments
We would like to thank our lifetime advisor and now colleague, V. V. Shokurov, for providing this classification question to the authors so long ago. It has inspired many years of fun and fruitful mathematics. In addition, the authors would like to thank V. Cheltsov for always motivating and encouraging the authors to continue in their work, and for his amazing ability to always make a global community feel local.
Citation
Joseph W. Cutrone. Nicholas A. Marshburn. "An Update on the Classification of Rank 2 Weak Fano Threefolds." Taiwanese J. Math. Advance Publication 1 - 13, 2025. https://doi.org/10.11650/tjm/250102
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