no. 1
Augmented and restricted base loci of cycles
[Lieux de base augmentés et restreints des cycles]
Lopez, Angelo Felice1
1 Dipartimento di Matematica e Fisica Università di Roma Tre Largo San Leonardo Murialdo 1 00146 Roma, (Italy)
Annales de l'Institut Fourier, Tome 72 (2022) no. 1, pp. 435-464.

Nous introduisons les lieux de base augmentés et restreints de cycles et nous étudions les propriétés de positivité naturellement définies par ces lieux de base.

We introduce augmented and restricted base loci of cycles and we study the positivity properties naturally defined by these base loci.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3458
Classification : 14C25, 14C10, 14J40
Keywords: base loci, cycles, positivity
Mot clés : lieux de base, cycles, positivité
Lopez, Angelo Felice 1

1 Dipartimento di Matematica e Fisica Università di Roma Tre Largo San Leonardo Murialdo 1 00146 Roma, (Italy)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{AIF_2022__72_1_435_0,
     author = {Lopez, Angelo Felice},
     title = {Augmented and restricted base loci of cycles},
     journal = {Annales de l'Institut Fourier},
     pages = {435--464},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {72},
     number = {1},
     year = {2022},
     doi = {10.5802/aif.3458},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3458/}
}
TY  - JOUR
AU  - Lopez, Angelo Felice
TI  - Augmented and restricted base loci of cycles
JO  - Annales de l'Institut Fourier
PY  - 2022
SP  - 435
EP  - 464
VL  - 72
IS  - 1
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.3458/
DO  - 10.5802/aif.3458
LA  - en
ID  - AIF_2022__72_1_435_0
ER  - 
%0 Journal Article
%A Lopez, Angelo Felice
%T Augmented and restricted base loci of cycles
%J Annales de l'Institut Fourier
%D 2022
%P 435-464
%V 72
%N 1
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.3458/
%R 10.5802/aif.3458
%G en
%F AIF_2022__72_1_435_0
Lopez, Angelo Felice. Augmented and restricted base loci of cycles. Annales de l'Institut Fourier, Tome 72 (2022) no. 1, pp. 435-464. doi : 10.5802/aif.3458. https://aif.centre-mersenne.org/articles/10.5802/aif.3458/

[1] Dang, Nguyen-Bac Degrees of Iterates of Rational Maps on Normal Projective Varieties (2019) (https://arxiv.org/abs/1701.07760)

[2] Debarre, Olivier; Ein, Lawrence; Lazarsfeld, Robert; Voisin, Claire Pseudoeffective and nef classes on abelian varieties, Compos. Math., Volume 147 (2011) no. 6, pp. 1793-1818 | DOI | MR | Zbl

[3] Ein, Lawrence; Lazarsfeld, Robert; Mustaţă, Mircea; Nakamaye, Michael; Popa, Mihnea Asymptotic invariants of base loci, Ann. Inst. Fourier, Volume 56 (2006) no. 6, pp. 1701-1734 | Numdam | MR | Zbl

[4] Ein, Lawrence; Lazarsfeld, Robert; Mustaţă, Mircea; Nakamaye, Michael; Popa, Mihnea Restricted volumes and base loci of linear series, Am. J. Math., Volume 131 (2009) no. 3, pp. 607-651 | DOI | MR | Zbl

[5] Eisenbud, David; Harris, Joe 3264 and all that. A second course in algebraic geometry, Cambridge University Press, 2016 | DOI | Zbl

[6] Fulger, Mihai; Lehmann, Brian Morphisms and faces of pseudo-effective cones, Proc. Lond. Math. Soc., Volume 112 (2016) no. 4, pp. 651-676 | DOI | MR | Zbl

[7] Fulger, Mihai; Lehmann, Brian Kernels of numerical pushforwards, Adv. Geom., Volume 17 (2017) no. 3, pp. 373-379 | DOI | MR | Zbl

[8] Fulger, Mihai; Lehmann, Brian Positive cones of dual cycle classes, Algebr. Geom., Volume 4 (2017) no. 1, pp. 1-28 | DOI | MR | Zbl

[9] Fulger, Mihai; Lehmann, Brian Zariski decompositions of numerical cycle classes, J. Algebr. Geom., Volume 26 (2017) no. 1, pp. 43-106 | DOI | MR | Zbl

[10] Fulton, William Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., Springer, 1998 | DOI | Zbl

[11] Grothendieck, Alexander Éléments de géométrie algébrique. II. Étude globale élémentaire de quelques classes de morphismes, Publ. Math., Inst. Hautes Étud. Sci., Volume 8 (1961), pp. 1-222 | Numdam | Zbl

[12] Hartshorne, Robin Algebraic geometry, Graduate Texts in Mathematics, 52, Springer, 1977 | DOI | Zbl

[13] Jager, Conner P. Representation Theory and Vector Bundles, Ph. D. Thesis, Department of Mathematics, Princeton University, Princeton, USA (2015) (Senior thesis, https://dataspace.princeton.edu/jspui/handle/88435/dsp01hx11xh55q)

[14] Kleiman, Steven L. Geometry on Grassmannians and applications to splitting bundles and smoothing cycles, Publ. Math., Inst. Hautes Étud. Sci., Volume 36 (1969), pp. 281-297 | DOI | Numdam | Zbl

[15] Lazarsfeld, Robert Positivity in algebraic geometry. I. Classical setting: line bundles and linear series, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., 48, Springer, 2004 | Zbl

[16] Maggesi, Marco; Vezzosi, Gabriele Some elementary remarks on lci algebraic cycles, Riv. Mat. Univ. Parma, Volume 9 (2018) no. 2, pp. 365-372 | MR | Zbl

[17] Nakayama, Noboru Zariski-decomposition and abundance, MSJ Memoirs, 14, Mathematical Society of Japan, 2004 | Zbl

[18] Ottem, John C. Ample subvarieties and q-ample divisors, Adv. Math., Volume 229 (2012) no. 5, pp. 2868-2887 | DOI | MR | Zbl

[19] Ottem, John C. On subvarieties with ample normal bundle, J. Eur. Math. Soc., Volume 18 (2016) no. 11, pp. 2459-2468 | DOI | MR | Zbl

[20] Ottem, John C. Nef cycles on some hyperkähler fourfolds (2019) (https://arxiv.org/abs/1505.01477)

[21] Pragacz, Piotr Symmetric polynomials and divided differences in formulas of intersection theory, Parameter spaces: Enumerative geometry, algebra and combinatorics. Proceedings of the Banach Center conference, Warsaw, Poland, February 1994 (Banach Center Publications), Volume 36, Institute of Mathematics of the Polish Academy of Sciences, 1996, pp. 125-177 | MR | Zbl

[22] Ross, Julius; Toma, Matei Hodge–Riemann bilinear relations for Schur classes of ample vector bundles (2021) (https://arxiv.org/abs/1905.13636)

[23] Stacks Project The Stacks Project, 2018 (http://stacks.math.columbia.edu/)

[24] Zariski, Oskar The theorem of Riemann–Roch for high multiples of an effective divisor on an algebraic surface, Ann. Math., Volume 76 (1962) no. 2, pp. 560-615 | DOI | MR | Zbl

Cité par Sources :