Lelong numbers on projective varieties

Rodrigo Parra[1]

  • [1] Department of Mathematics, University of Michigan. 530 Church Street, Ann Arbor, MI 48109-1043 USA

Annales de la faculté des sciences de Toulouse Mathématiques (2011)

  • Volume: 20, Issue: 4, page 781-800
  • ISSN: 0240-2963

Abstract

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Given a positive closed (1,1)-current T defined on the regular locus of a projective variety X with bounded mass near the singular part of X and Y an irreducible algebraic subset of X , we present uniform estimates for the locus inside Y where the Lelong numbers of T are larger than the generic Lelong number of T along Y .

How to cite

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Parra, Rodrigo. "Lelong numbers on projective varieties." Annales de la faculté des sciences de Toulouse Mathématiques 20.4 (2011): 781-800. <http://eudml.org/doc/219710>.

@article{Parra2011,
abstract = {Given a positive closed (1,1)-current $T$ defined on the regular locus of a projective variety $X$ with bounded mass near the singular part of $X$ and $Y$ an irreducible algebraic subset of $X$, we present uniform estimates for the locus inside $Y$ where the Lelong numbers of $T$ are larger than the generic Lelong number of $T$ along $Y$.},
affiliation = {Department of Mathematics, University of Michigan. 530 Church Street, Ann Arbor, MI 48109-1043 USA},
author = {Parra, Rodrigo},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Lelong numbers; positive closed currents; algebraic sets; projective variety},
language = {eng},
month = {7},
number = {4},
pages = {781-800},
publisher = {Université Paul Sabatier, Toulouse},
title = {Lelong numbers on projective varieties},
url = {http://eudml.org/doc/219710},
volume = {20},
year = {2011},
}

TY - JOUR
AU - Parra, Rodrigo
TI - Lelong numbers on projective varieties
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2011/7//
PB - Université Paul Sabatier, Toulouse
VL - 20
IS - 4
SP - 781
EP - 800
AB - Given a positive closed (1,1)-current $T$ defined on the regular locus of a projective variety $X$ with bounded mass near the singular part of $X$ and $Y$ an irreducible algebraic subset of $X$, we present uniform estimates for the locus inside $Y$ where the Lelong numbers of $T$ are larger than the generic Lelong number of $T$ along $Y$.
LA - eng
KW - Lelong numbers; positive closed currents; algebraic sets; projective variety
UR - http://eudml.org/doc/219710
ER -

References

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  3. Demailly (J.-P.).— A numerical criterion for very ample line bundles. J. Differential Geom., 37(2), p. 323-374 (1993). Zbl0783.32013MR1205448
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  6. Dinh (T-C) and Sibony (N.).— Equidistribution towards the Green current for holomorphic maps, Ann. Sci. Éc. Norm. Supér. (4) 41 (2008), no. 2, p. 307-336. (2468484 (2009i:32041) Zbl1160.32029MR2468484
  7. Lazarsfeld (R.).— Positivity in algebraic geometry. I, volume 48 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Springer-Verlag, Berlin, 2004. Classical setting: line bundles and linear series. Zbl1093.14500MR2095471
  8. Meo (M.).— Inégalités d’auto-intersection pour les courants positifs fermés définis dans les variétés projectives. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 26, p. 161-184 (1998). Zbl0914.32013MR1632996
  9. Yum Tong Siu.— Analyticity of sets associated to Lelong numbers and the extension of closed positive currents. Invent. Math., 27, p. 53-156 (1974). Zbl0289.32003MR352516
  10. Varolin (D.).— Three variations on a theme in complex analytic geometry (lecture notes). http://www.math.sunysb.edu/ dror/. Zbl1222.32001MR2743817
  11. Vigny (G.).— Lelong-Skoda transform for compact Kähler manifolds and self-intersection inequalities. J. Geom. Anal., 19, p. 433-451 (2009). Zbl1173.32014MR2481969

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