Born in Kibbutz Ein-Shemer, Israel in 1951. He studied at the Israeli Sate Art Teachers' TrainingCollege in Ramat HaSharon, where he now himself teaches.
He has had numerous one-person exhibitions in Israel, including the Israel and TelAvivMuseums, and in the United States, including Boston's Institute of Contemporary Art. Geva has also shown in Haifa (Haifa Museum), Sao Paulo (at the city museums and in the 18th Bienal), Antwerp (Royal Museum of Fine Arts), New York (Jewish Museum, Grey Art Gallery of New York University), Philadelphia, Zurich (Kunsthaus), Hannover (Orangerie Herrenhausen), Dusseldorf (Kunsthalle), Marsala Sicily, Berlin, Houston, Dresden, Cahpel Hill North Carolina, Miami Beach (Bass Art Musuem), Madrid, Helsinki, and Lund Sweden.
The IsraelMuseum presented him with the Koliner Young Artist Award in 1985. He won the Science and Art Minister's Prize for visual art in 1994, and was awarded the Isracart Prize by the Tel Aviv Museum of Art in 1996.