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We study the Zariski closure of the monodromy group   Mon   of Lauricella's hypergeometric function    F  C   . If the identity component    Mon  0    acts irreducibly, thenMon  ¯   ∩   SL   2  n(  C  )must be one of classical groupsSL   2  n(  C  )   ,   SO   2  n(  C  )andSp   2  n(  C  )    . We also study Calabi–Yau varieties arising from integral representations of    F  C   .

Picard–Vessiot groups of Lauricella's hypergeometric systems E C and Calabi–Yau varieties arising integral representations