Infinitesimal Torelli theorem for surfaces with c_1^2=3, \chi=2, and the torsion group Z/3

We prove the infinitesimal Torelli theorem for general minimal complex surfaces X’s with the first Chern number 3, the geometric genus 1, and the irregularity 0 which have non-trivial 3-torsion divisors. We also show that the coarse moduli space for surfaces with the invariants as above is a 14-dimensional unirational variety.