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Computation and Data in the Classification of Fano Varieties

In: Nankai Symposium on Mathematical Dialogues

Author

Listed:
  • 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)

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.

Suggested Citation

  • Gavin Brown & Tom Coates & Alessio Corti & Tom Ducat & Liana Heuberger & Alexander M. Kasprzyk, 2026. "Computation and Data in the Classification of Fano Varieties," Springer Books, in: Yang-Hui He & Mo-Lin Ge & Cheng-Ming Bai & Jiakang Bao & Edward Hirst (ed.), Nankai Symposium on Mathematical Dialogues, pages 93-108, Springer.
    • Handle: RePEc:spr:sprchp:978-981-19-2328-9_11
    DOI: 10.1007/978-981-19-2328-9_11
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