Topotecan in Treating Patients With Advanced Ovarian Epithelial, Fallopian Tube, or Primary Peritoneal Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed ovarian epithelial, fallopian tube, or primary peritoneal serous cancer * Stage IIIB, IIIC, or IV * Surgically staged and debulked * Complete clinical response after first-line platinum-based chemotherapy (cisplatin or carboplatin) defined by all of the following criteria: * No evidence of cancer by history or physical examination * CA 125 no greater than 35 units/mL * No evidence of residual cancer on CT scan of the abdomen/pelvis and chest x-ray * Must have received at least 5 courses of first-line chemotherapy PATIENT CHARACTERISTICS: Age * 18 and over Performance status * ECOG 0-2 Life expectancy * Not specified Hematopoietic * Granulocyte count at least 1,200/mm\^3 * Platelet count at least 90,000/mm\^3 Hepatic * Bilirubin normal * ALT and AST less than 1.5 times upper limit of normal (ULN) * Alkaline phosphatase less than 1.5 ULN Renal * Creatinine clearance at least 60 mL/min PRIOR CONCURRENT THERAPY: Biologic therapy * No concurrent immunotherapy Chemotherapy * See Disease Characteristics * At least 3 weeks since prior first-line chemotherapy * At least 3 years since other prior chemotherapy (other than first-line chemotherapy for ovarian, fallopian tube, or primary peritoneal cancer) * No other concurrent chemotherapy Endocrine therapy * No concurrent hormonal therapy Radiotherapy * No prior abdominopelvic radiotherapy * No concurrent radiotherapy Surgery * See Disease Characteristics * No concurrent surgery Other * No other concurrent antitumor therapy