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The Fermi surface as a contour of the gapless quasiparticle excitation in momentum space is studied based on a mean-field theory of the doped Mott insulator, where the underlying pseudogap phase is characterized by a two-component resonating-valence-bond (RVB) order that vanishes in the overdoping at $δ>δ^*$. Here the quasiparticle emerges as a ``collective'' mode and a Fermi arc is naturally present in the pseudogap regime, while a full Fermi surface is recovered at $δ>δ^*$. The area enclosed by the gapless quasiparticle contour still satisfies the Luttinger volume in both cases, and the ``Fermi arc'' at $δ<δ^*$ is actually due to a significant reduction of the spectral weight caused by a quasiparticle fractionalization in the antinodal region. The endpoints of the Fermi arcs exhibit enhanced density of states or ``hotspots'', which can further give rise to a charge-density-wave-like quasiparticle interference pattern. At the critical doping $δ^*$, the fractionalized spin excitations become gapless and incoherent which is signaled by a divergent specific heat. At $δ>δ^*$, the quasiparticle excitation restores the coherence over the full Fermi surface, but the fractionalization still persists at a higher energy/temperature which may be responsible for a strange metal behavior. Different mechanisms for the Fermi arc and experimental comparisons are briefly discussed.