Ulrich bundles on blowing up (and an erratum)

Gianfranco Casnati; Yeongrak Kim

doi:10.1016/j.crma.2017.09.020

Algebraic geometry

Ulrich bundles on blowing up (and an erratum)
[Fibrés de Ulrich sur les éclatements (et un erratum)]

Présenté par : Claire Voisin

Gianfranco Casnati ¹ ; Yeongrak Kim ²

¹ Dipartimento di Scienze Mathematiche, Politecnico di Torino, c.so Duca degli Abruzzi 24, 10129 Torino, Italy
² Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany

Comptes Rendus. Mathématique, Volume 355 (2017) no. 12, pp. 1291-1297.

Résumé
Abstract

Nous décrivons le comportement des faisceaux d'Ulrich en ce qui concerne leur image directe et réciproque par rapport aux éclatements des points. Nous corrigeons aussi un énoncé incorrect dans [11].

We deal with the behaviour of Ulrich bundles with respect to push-forward and pull-back via blowing-up points. We also correct a wrong statement in [11].

Reçu le : 2017-05-25
Accepté le : 2017-09-11
Publié le : 2017-11-13

DOI : 10.1016/j.crma.2017.09.020

Affiliations des auteurs :

Gianfranco Casnati ¹ ; Yeongrak Kim ²

¹ Dipartimento di Scienze Mathematiche, Politecnico di Torino, c.so Duca degli Abruzzi 24, 10129 Torino, Italy
² Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany

@article{CRMATH_2017__355_12_1291_0,
     author = {Gianfranco Casnati and Yeongrak Kim},
     title = {Ulrich bundles on blowing up (and an erratum)},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1291--1297},
     publisher = {Elsevier},
     volume = {355},
     number = {12},
     year = {2017},
     doi = {10.1016/j.crma.2017.09.020},
     language = {en},
}

TY  - JOUR
AU  - Gianfranco Casnati
AU  - Yeongrak Kim
TI  - Ulrich bundles on blowing up (and an erratum)
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 1291
EP  - 1297
VL  - 355
IS  - 12
PB  - Elsevier
DO  - 10.1016/j.crma.2017.09.020
LA  - en
ID  - CRMATH_2017__355_12_1291_0
ER  -

%0 Journal Article
%A Gianfranco Casnati
%A Yeongrak Kim
%T Ulrich bundles on blowing up (and an erratum)
%J Comptes Rendus. Mathématique
%D 2017
%P 1291-1297
%V 355
%N 12
%I Elsevier
%R 10.1016/j.crma.2017.09.020
%G en
%F CRMATH_2017__355_12_1291_0

Gianfranco Casnati; Yeongrak Kim. Ulrich bundles on blowing up (and an erratum). Comptes Rendus. Mathématique, Volume 355 (2017) no. 12, pp. 1291-1297. doi : 10.1016/j.crma.2017.09.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.020/

Bibliographie
Cité par

[1] J. Alexander Surfaces rationelles non spéciales dans $P^{4}$ , Math. Z., Volume 200 (1988), pp. 87-110

[2] M. Aprodu; G. Farkas; A. Ortega Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces, J. Reine Angew. Math., Volume 730 (2017), pp. 225-249

[3] I. Bauer Inner projections of algebraic surfaces: a finiteness result, J. Reine Angew. Math., Volume 460 (1995), pp. 1-13

[4] G. Casnati Rank 2 stable Ulrich bundles on anticanonically embedded surfaces, Bull. Aust. Math. Soc., Volume 95 (2017), pp. 22-37

[5] G. Casnati Special Ulrich bundles on non-special surfaces with $p_{g} = q = 0$ , Int. J. Math., Volume 28 (2017)

[6] G. Casnati; M. Filip; F. Malaspina Rank two aCM bundles on the del Pezzo threefold of degree 7, Rev. Mat. Complut., Volume 30 (2017), pp. 129-165

[7] P. Coronica Semistable Vector Bundles on Bubble Tree Surfaces, SISSA–Université Lille-1, 2015 (PhD thesis)

[8] D. Eisenbud; F.-O. Schreyer; J. Weyman Resultants and Chow forms via exterior syzigies, J. Amer. Math. Soc., Volume 16 (2003), pp. 537-579

[9] R. Hartshorne Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, Springer-Verlag, 1977

[10] J. Herzog; B. Ulrich; J. Backelin Linear maximal Cohen–Macaulay modules over strict complete intersections, J. Pure Appl. Algebra, Volume 71 (1991), pp. 187-202

[11] Y. Kim Ulrich bundles on blowing ups, C. R. Acad. Sci. Paris, Ser. I, Volume 354 (2016), pp. 1215-1218

[12] A. Lopez Noether–Lefschetz Theory and the Picard Group of Projective Surfaces, Memoirs of the AMS, vol. 89, 1991

[13] R.L.E. Schwarzenberger Vector bundles on algebraic surfaces, Proc. Lond. Math. Soc., Volume 11 (1961), pp. 601-622

Cité par Sources :

Commentaires - Politique