Combination Chemotherapy in Treating Patients With Ovarian Epithelial, Fallopian Tube, or Peritoneal Cancer

DISEASE CHARACTERISTICS: Histologically confirmed stage IC-IV ovarian epithelial, fallopian tube, or peritoneal carcinoma No tumors of low-malignant potential (borderline tumors) No symptomatic brain metastases PATIENT CHARACTERISTICS: Age: 18 and over Performance status: ECOG 0-2 OR Karnofsky 70-100% Life expectancy: At least 6 months Hematopoietic: WBC at least 3,000/mm^3 Absolute neutrophil count at least 1,500/mm^3 Platelet count at least 100,000/mm^3 Hemoglobin greater than 10 g/dL Hepatic: Bilirubin no greater than 2 times upper limit of normal Renal: Glomerular filtration rate at least 60 mL/min Cardiovascular: No history of congestive heart failure (New York Heart Association class III or IV heart disease) even if medically controlled No myocardial infarction within the past 6 months No history of atrial or ventricular arrhythmias Neurologic: No history of seizure disorder No history of CNS disorder No pre-existing motor or sensory neuropathy or symptoms grade 2 or greater Other: No severe concurrent infection No prior hypersensitivity reaction to products containing Cremophor EL or compounds chemically related to carboplatin, paclitaxel, or gemcitabine No complete bowel obstruction No other concurrent severe medical problems that would preclude study Not pregnant or nursing Negative pregnancy test Fertile patients must use effective contraception PRIOR CONCURRENT THERAPY: Biologic therapy: No concurrent immunotherapy No concurrent WBC transfusions Chemotherapy: No prior chemotherapy No other concurrent chemotherapy Endocrine therapy: No concurrent hormonal therapy except replacement therapy or steroid antiemetics Radiotherapy: No prior radiotherapy No concurrent radiotherapy Surgery: No more than 6 weeks since prior definitive surgery