  By the reduced component in a moduli space of stable quasimaps to
n-dimensional projective space we mean the closure of the locus in which the
domain curves are smooth. As in the moduli space of stable maps, we prove the
reduced component is smooth in genus 2, degree greater or equal to 3.
  Then we prove the virtual fundamental cycle of the moduli space of stable
quasimaps to a complete intersection X in the projective space of genus 2,
degree greater or equal to 3 is explicitly expressed in terms of the
fundamental cycle of the reduced component of the projective space and virtual
cycles of lower genus moduli spaces of X.
