Mather discrepancy and the arc spaces

Shihoko Ishii[1]

  • [1] Graduate School of Mathematical Science University of Tokyo Komaba, Meguro, Tokyo (Japan)

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 1, page 89-111
  • ISSN: 0373-0956

Abstract

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A goal of this paper is a characterization of singularities according to a new invariant, Mather discrepancy. We also show some evidences convincing us that Mather discrepancy is a reasonable invariant in a view point of birational geometry.

How to cite

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Ishii, Shihoko. "Mather discrepancy and the arc spaces." Annales de l’institut Fourier 63.1 (2013): 89-111. <http://eudml.org/doc/275638>.

@article{Ishii2013,
abstract = {A goal of this paper is a characterization of singularities according to a new invariant, Mather discrepancy. We also show some evidences convincing us that Mather discrepancy is a reasonable invariant in a view point of birational geometry.},
affiliation = {Graduate School of Mathematical Science University of Tokyo Komaba, Meguro, Tokyo (Japan)},
author = {Ishii, Shihoko},
journal = {Annales de l’institut Fourier},
keywords = {Singularities; arc space; minimal log-discrepancy; singularities},
language = {eng},
number = {1},
pages = {89-111},
publisher = {Association des Annales de l’institut Fourier},
title = {Mather discrepancy and the arc spaces},
url = {http://eudml.org/doc/275638},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Ishii, Shihoko
TI - Mather discrepancy and the arc spaces
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 1
SP - 89
EP - 111
AB - A goal of this paper is a characterization of singularities according to a new invariant, Mather discrepancy. We also show some evidences convincing us that Mather discrepancy is a reasonable invariant in a view point of birational geometry.
LA - eng
KW - Singularities; arc space; minimal log-discrepancy; singularities
UR - http://eudml.org/doc/275638
ER -

References

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  11. Shihoko Ishii, Jet schemes, arc spaces and the Nash problem, C. R. Math. Acad. Sci. Soc. R. Can. 29 (2007), 1-21 Zbl1162.14006MR2354631
  12. Shihoko Ishii, Maximal divisorial sets in arc spaces, Algebraic geometry in East Asia—Hanoi 2005 50 (2008), 237-249, Math. Soc. Japan, Tokyo Zbl1162.14022MR2409559
  13. Shihoko Ishii, János Kollár, The Nash problem on arc families of singularities, Duke Math. J. 120 (2003), 601-620 Zbl1052.14011MR2030097
  14. Masayuki Kawakita, Inversion of adjunction on log canonicity, Invent. Math. 167 (2007), 129-133 Zbl1114.14009MR2264806
  15. Masayuki Kawakita, On a comparison of minimal log discrepancies in terms of motivic integration, J. Reine Angew. Math. 620 (2008), 55-65 Zbl1151.14014MR2427975
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