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2025 An Update on the Classification of Rank 2 Weak Fano Threefolds
Joseph W. Cutrone, Nicholas A. Marshburn
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Taiwanese J. Math. Advance Publication 1-13 (2025). DOI: 10.11650/tjm/250102

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

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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

Information

Published: 2025
First available in Project Euclid: 22 January 2025

Digital Object Identifier: 10.11650/tjm/250102

Subjects:
Primary: 14-XX

Keywords: 2-ray diagram , almost Fano threefold , central models , Fano threefold , Sarkisov links , weak Fano threefold

Rights: Copyright © 2025 The Mathematical Society of the Republic of China

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