A turbomachine compressor module, comprising an annular array of structural arms defining inter-arm spaces between two circumferentially adjacent arms; and an annular array of stator vanes with variable orientation about a respective axis (A) and disposed at least partially within the inter-arm spaces. The arms are provided with flaps pivotable about a respective axis (B). Also, a turbomachine provided with such a module and a row of rotor blades directly downstream of the module.