Singularities, the Space of Arcs and Applications to Birational Geometry

Shihoko Ishii ()
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Shihoko Ishii: The University of Tokyo

Chapter Chapter 3 in Handbook of Geometry and Topology of Singularities IV, 2023, pp 161-210 from Springer

Abstract: 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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-31925-9_3

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DOI: 10.1007/978-3-031-31925-9_3

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