The role of the Ellingsrud-Strømme construction in the classification of instantons
Laurent Gruson ; Frédéric Han
Open Mathematics, Tome 10 (2012), p. 1188-1197 / Harvested from The Polish Digital Mathematics Library

We review a construction of Ellingsrud-Strømme relating instantons of charge n on the ordinary projective space and theta-characteristics on a plane curve of degree n with some extra-structure.

Publié le : 2012-01-01
EUDML-ID : urn:eudml:doc:269320
@article{bwmeta1.element.doi-10_2478_s11533-012-0015-9,
     author = {Laurent Gruson and Fr\'ed\'eric Han},
     title = {The role of the Ellingsrud-Str\o mme construction in the classification of instantons},
     journal = {Open Mathematics},
     volume = {10},
     year = {2012},
     pages = {1188-1197},
     zbl = {1282.14073},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0015-9}
}
Laurent Gruson; Frédéric Han. The role of the Ellingsrud-Strømme construction in the classification of instantons. Open Mathematics, Tome 10 (2012) pp. 1188-1197. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0015-9/

[1] Barth W., Moduli of vector bundles on the projective plane, Invent. Math., 1977, 42, 63–91 http://dx.doi.org/10.1007/BF01389784 | Zbl 0386.14005

[2] Barth W., Some properties of stable rank-2 vector bundles on ℙn, Math. Ann., 1977, 226(2), 125–150 http://dx.doi.org/10.1007/BF01360864 | Zbl 0332.32021

[3] Böhmer W., Trautmann G., Special instanton bundles and Poncelet curves, In: Singularities, Representation of Algebras and Vector Bundles, Lambrecht, December 13–17, 1985, Lecture Notes in Math., 1273, Springer, Berlin, 1987, 325–336 http://dx.doi.org/10.1007/BFb0078852

[4] Ellingsrud G., Strømme S.A., Stable rank-2 vector bundles on ℙ3 with c 1 = 0 and c 2 = 3, Math. Ann., 1981, 255(1), 123–135 http://dx.doi.org/10.1007/BF01450561 | Zbl 0438.14009

[5] Gruson L., Skiti M., 3-instantons et réseaux de quadriques, Math. Ann., 1994, 298(2), 253–273 http://dx.doi.org/10.1007/BF01459736 | Zbl 0810.14008

[6] Han F., Codimension du schéma des multisauteuses d’un 4- ou 5-instanton, PhD thesis, Université de Lille 1, 1996

[7] Landsberg J.M., Manivel L., Generalizations of Strassen’s equations for secant varieties of Segre varieties, Comm. Algebra, 2008, 36(2), 405–422 http://dx.doi.org/10.1080/00927870701715746 | Zbl 1137.14038

[8] Macdonald I.G., Symmetric Functions and Hall Polynomials, Oxford Math. Monogr., Clarendon Press, Oxford University Press, New York, 1995 | Zbl 0824.05059

[9] Ottaviani G., Symplectic bundles on the plane, secant varieties and Lüroth quartics revisited, In: Vector Bundles and Low Codimensional Subvarieties: State of the Art and Recent Developments, Povo-Trento, September 11–16, 2006, Quad. Mat., 21, Seconda Università degli Studi di Napoli, Caserta, 2007, 315–352

[10] Sorger C., Thêta-caractéristiques des courbes tracées sur une surface lisse, J. Reine Angew. Math., 1993, 435, 83–118

[11] Tjurin A.N., On the superpositions of mathematical instantons, In: Arithmetic and Geometry. II, Progr. Math., 36, Birkhäuser, Boston, 1983, 433–450

[12] Vallès J., Fibrés de Schwarzenberger et coniques de droites sauteuses, Bull. Soc. Math. France, 2000, 128(3), 433–449 | Zbl 0955.14009

[13] Weyman J., Cohomology of Vector Bundles and Syzygies, Cambridge Tracts in Math., 149, Cambridge University Press, Cambridge, 2003 http://dx.doi.org/10.1017/CBO9780511546556