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Transport and torque magnetometry measurements are performed at high magneticfields and low temperatures in a series of p-type (Ca-doped) Bi$_{2}$Se$_{3}$crystals. The angular dependence of the Shubnikov-de Haas and de Haas-vanAlphen quantum oscillations enables us to determine the Fermi surface of thebulk valence band states as a function of the carrier density. At low density,the angular dependence exhibits a downturn in the oscillations frequencybetween $0^\circ$ and $90^\circ$, reflecting a bag-shaped hole Fermi surface.The detection of a single frequency for all tilt angles rules out the existenceof a Fermi surface with different extremal cross-sections down to $24$~meV.There is therefore no signature of a camel-back in the valence band of our bulksamples, in accordance with the direct band gap predicted by $GW$ calculations.

The hole Fermi surface in Bi$_{2}$Se$_{3}$ probed by quantum oscillations