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