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Singularities, the Space of Arcs and Applications to Birational Geometry

In: Handbook of Geometry and Topology of Singularities IV

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  • Shihoko Ishii

    (The University of Tokyo)

Abstract

This paper is an introduction to the space of arcs and the space of jets of an algebraic variety. We also introduce the Nash problem on arc families, which makes a bridge between the theory of the space of arcs and the theory of birational geometry. We then focus on applications of the space of arcs to the theory of birational geometry and show the recent results.

Suggested Citation

  • Shihoko Ishii, 2023. "Singularities, the Space of Arcs and Applications to Birational Geometry," Springer Books, in: José Luis Cisneros-Molina & Lê Dũng Tráng & José Seade (ed.), Handbook of Geometry and Topology of Singularities IV, chapter 0, pages 161-210, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-31925-9_3
    DOI: 10.1007/978-3-031-31925-9_3
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