no. 12
Algebraic geometry
Ulrich bundles on blowing up (and an erratum)
[Fibrés de Ulrich sur les éclatements (et un erratum)]

Présenté par : Claire Voisin

Casnati, Gianfranco1 ; Kim, Yeongrak2
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, Tome 355 (2017) no. 12, pp. 1291-1297.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.09.020
Casnati, Gianfranco 1 ; Kim, Yeongrak 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 = {Casnati, Gianfranco and Kim, Yeongrak},
     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},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2017.09.020/}
}
TY  - JOUR
AU  - Casnati, Gianfranco
AU  - Kim, Yeongrak
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
UR  - http://www.numdam.org/articles/10.1016/j.crma.2017.09.020/
DO  - 10.1016/j.crma.2017.09.020
LA  - en
ID  - CRMATH_2017__355_12_1291_0
ER  - 
%0 Journal Article
%A Casnati, Gianfranco
%A Kim, Yeongrak
%T Ulrich bundles on blowing up (and an erratum)
%J Comptes Rendus. Mathématique
%D 2017
%P 1291-1297
%V 355
%N 12
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2017.09.020/
%R 10.1016/j.crma.2017.09.020
%G en
%F CRMATH_2017__355_12_1291_0
Casnati, Gianfranco; Kim, Yeongrak. Ulrich bundles on blowing up (and an erratum). Comptes Rendus. Mathématique, Tome 355 (2017) no. 12, pp. 1291-1297. doi : 10.1016/j.crma.2017.09.020. http://www.numdam.org/articles/10.1016/j.crma.2017.09.020/

[1] Alexander, J. Surfaces rationelles non spéciales dans P4, Math. Z., Volume 200 (1988), pp. 87-110

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

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

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

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

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

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

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

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

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

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

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

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

Cité par Sources :