Geodesic
Analogs of Torelli's theorem for multidimensional vector bundles over an arbitrary algebraic curve
Izvestiya. Mathematics , Tome 4 (1970) no. 2, pp. 343-370.

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It is prored that the space of moduli of stable bundles over a curve with fixed determinant and relatively prime degree and dimension uniquely determines the curve. 
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A. N. Tyurin. Analogs of Torelli's theorem for multidimensional vector bundles over an arbitrary algebraic curve. Izvestiya. Mathematics , Tome 4 (1970) no. 2, pp. 343-370. http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a4/

[1] Vinogradov I. M., Osnovy teorii chisel, Nauka, M., 1965 | MR

[2] Mumford D., “Picard groups of module problems”, Proc. Conf. Arith. Alg. Geom. Harper and Row, 1966, 33–82 | MR

[3] Mumford D., Newstead P., “Periods of a moduli space of bundles on curves”, Amer. J. Math., XC:4 (1968), 1200–1208 | DOI | MR

[4] Newstead P. E., “Stable bundles of rank 2 and odd degree over a curve of genus 2”, Topology, 7 (1968), 205–215 | DOI | MR | Zbl

[5] Tyurin A. H., “Analog teoremy Torelli dlya dvumernykh rassloenii nad algebraicheskoi krivoi proizvolnogo roda”, Izv. AN SSSR. Ser. matem., 33 (1969), 1149–1170 | MR | Zbl

[6] Schwarzenberger R. L. E., “Vector bundles on algebraic surfaces”, Proc. London Math. Soc., 11:44 (1961), 623–640 | DOI | MR | Zbl