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Une involution sur un espace de modules de fibrés instantons. (An involution on a moduli space of instanton bundles). (French) Zbl 0964.14018
Summary: We describe an involution on the moduli space of instanton bundles with Chern classes \(c_1=0\), \(c_2=4\). We use this involution to construct elliptic \(K_3\) surfaces with two surjective morphisms to the projective line. These are the smooth quartic surfaces of \(\mathbb{P}^3\) with a morphism of degree 32 to \(\mathbb{P}^\times\mathbb{P}^1\).

MSC:
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14J27 Elliptic surfaces, elliptic or Calabi-Yau fibrations
14J28 \(K3\) surfaces and Enriques surfaces
14M12 Determinantal varieties
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References:
[1] D’ALMEIDA (J.) . - Courbes de l’espace projectif , J. reine angew Math., t. 370, 1986 , p. 30-51. Article | MR 87k:14034 | Zbl 0585.14010 · Zbl 0585.14010 · doi:10.1515/crll.1986.370.30 · crelle:GDZPPN002203820 · eudml:152858
[2] BARTH (W.) . - Irreducibility of the space of mathematical instanton with rank 2 and c2 = 4 , Math. Ann., t. 258, 1981 , p. 81-106. MR 84a:14010 | Zbl 0477.14014 · Zbl 0477.14014 · doi:10.1007/BF01450348 · eudml:163580
[3] FULTON (W.) . - Intersection Theory . - Springer Verlag, 1984 . MR 85k:14004 | Zbl 0541.14005 · Zbl 0541.14005
[4] HARTSHORNE (R.) . - Stable vector bundles of rank 2 on \Bbb P\(^{3}\) , Math. Ann., t. 238, 1978 , p. 229-280. MR 80c:14011 | Zbl 0411.14002 · Zbl 0411.14002 · doi:10.1007/BF01420250 · eudml:163199
[5] KLEIMAN (S.) . - The transversality of a general translate , Compositio Math., t. 38, 1974 , p. 287-297. Numdam | MR 50 #13063 | Zbl 0288.14014 · Zbl 0288.14014 · numdam:CM_1974__28_3_287_0 · eudml:89215
[6] LE POTIER (J.) . - Sur l’espace des modules des fibrés de Yang Mills , Mathématiques et Physique, Séminaire École Normale Supérieure 1979 - 1982 , Birkhaüser, 1983 . Zbl 0532.14003 · Zbl 0532.14003
[7] PESKINE (C.) , SZPIRO (L.) . - Liaison des variétés algébriques , Inv. Math., t. 26, 1974 , p. 271-302. MR 51 #526 | Zbl 0298.14022 · Zbl 0298.14022 · doi:10.1007/BF01425554 · eudml:142303
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