Local volumes of Cartier divisors over normal algebraic varieties

Mihai Fulger[1]

  • [1] Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA Institute of Mathematics of the Romanian Academy, P. O. Box 1-764, RO-014700, Bucharest, Romania

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 5, page 1793-1847
  • ISSN: 0373-0956

Abstract

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In this paper we study a notion of local volume for Cartier divisors on arbitrary blow-ups of normal complex algebraic varieties of dimension greater than one, with a distinguished point. We apply this to study an invariant for normal isolated singularities, generalizing a volume defined by J. Wahl for surfaces. We also compare this generalization to a different one arising in recent work of T. de Fernex, S. Boucksom, and C. Favre.

How to cite

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Fulger, Mihai. "Local volumes of Cartier divisors over normal algebraic varieties." Annales de l’institut Fourier 63.5 (2013): 1793-1847. <http://eudml.org/doc/275667>.

@article{Fulger2013,
abstract = {In this paper we study a notion of local volume for Cartier divisors on arbitrary blow-ups of normal complex algebraic varieties of dimension greater than one, with a distinguished point. We apply this to study an invariant for normal isolated singularities, generalizing a volume defined by J. Wahl for surfaces. We also compare this generalization to a different one arising in recent work of T. de Fernex, S. Boucksom, and C. Favre.},
affiliation = {Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA Institute of Mathematics of the Romanian Academy, P. O. Box 1-764, RO-014700, Bucharest, Romania},
author = {Fulger, Mihai},
journal = {Annales de l’institut Fourier},
keywords = {Local volumes; Hilbert-Samuel multiplicity; plurigenera; asymptotic invariants; Okounkov body; local volumes},
language = {eng},
number = {5},
pages = {1793-1847},
publisher = {Association des Annales de l’institut Fourier},
title = {Local volumes of Cartier divisors over normal algebraic varieties},
url = {http://eudml.org/doc/275667},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Fulger, Mihai
TI - Local volumes of Cartier divisors over normal algebraic varieties
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 5
SP - 1793
EP - 1847
AB - In this paper we study a notion of local volume for Cartier divisors on arbitrary blow-ups of normal complex algebraic varieties of dimension greater than one, with a distinguished point. We apply this to study an invariant for normal isolated singularities, generalizing a volume defined by J. Wahl for surfaces. We also compare this generalization to a different one arising in recent work of T. de Fernex, S. Boucksom, and C. Favre.
LA - eng
KW - Local volumes; Hilbert-Samuel multiplicity; plurigenera; asymptotic invariants; Okounkov body; local volumes
UR - http://eudml.org/doc/275667
ER -

References

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