Computation and Data in the Classification of Fano Varieties

Gavin Brown (), Tom Coates (), Alessio Corti (), Tom Ducat (), Liana Heuberger () and Alexander M. Kasprzyk ()
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Gavin Brown: University of Warwick, Mathematics Institute
Tom Coates: Imperial College London, Department of Mathematics
Alessio Corti: Imperial College London, Department of Mathematics
Tom Ducat: Durham University, Department of Mathematical Sciences
Liana Heuberger: Institut de Mathématiques de Marseille
Alexander M. Kasprzyk: University of Warwick, Mathematics Institute

A chapter in Nankai Symposium on Mathematical Dialogues, 2026, pp 93-108 from Springer

Abstract: Abstract Fano varieties are ‘atomic pieces’ of algebraic varieties, the shapes that can be defined by polynomial equations. We describe the role of computation and database methods in the construction and classification of Fano varieties, with an emphasis on three-dimensional Fano varieties with mild singularities called $$\mathbb {Q}$$ Q -Fano threefolds. The classification of $$\mathbb {Q}$$ Q -Fano threefolds has been open for several decades, but there has been significant recent progress. These advances combine computational algebraic geometry and large-scale data analysis with new ideas that originated in theoretical physics.

Keywords: Fano variety; Mirror symmetry; Classification (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-981-19-2328-9_11

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