Comptes Rendus
Algebraic geometry
Ulrich bundles on blowing up (and an erratum)
[Fibrés de Ulrich sur les éclatements (et un erratum)]
Comptes Rendus. Mathématique, Volume 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
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
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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/

[1] J. Alexander Surfaces rationelles non spéciales dans P4, 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 pg=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

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