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Fourier functor and its application to the moduli of bundles on an abelian variety. (English) Zbl 0672.14025

Algebraic geometry, Proc. Symp., Sendai/Jap. 1985, Adv. Stud. Pure Math. 10, 515-550 (1987).
[For the entire collection see Zbl 0628.00007.]
We talk on the vector bundles on a K3 surface and applications to the geometry of a K3 surface. Most content of our talk is contained in the paper “On the moduli space of bundles on K3 surfaces, I” [Vector bundles on algebraic varieties, Pap. Colloq., Bombay 1984, Stud. Math., Tata Inst. Fundam. Res. 11, 341-413 (1987)]. In this article we discuss the vector bundles on an abelian variety instead.
In our paper in Nagoya Math. J. 81, 153-175 (1981; Zbl 0417.14036)], we have defined the Fourier functor and shown its basic properties. This functor is a powerful tool for investigating the vector bundle on an abelian variety. In this article, we shall show that a sheaf and its Fourier transform have the same local (in the Zariski topology) moduli space and apply this to the study of the moduli space of vector bundles on an abelian variety X.

MSC:

14K10 Algebraic moduli of abelian varieties, classification
14D20 Algebraic moduli problems, moduli of vector bundles
43A32 Other transforms and operators of Fourier type
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14J28 \(K3\) surfaces and Enriques surfaces