Infinitesimal Torelli Theorem for regular surfaces with very ample   canonical divisor
  The article proves the Infinitesimal Torelli theorem for surfaces subject to the following conditions:   1) the canonical bundle of a surface is ample and generated by its global sections,   2)the geometric genus $p_g \geq 4$,   3) the irregularity $q=0$ .   The main novelty is a realization of the Kodaira-Spencer classes lying in the kernel of the cohomology cup-product controlling the derivative of the period map of weight 2 in the category of the coherent sheaves of a surface. 
Igor Reider
math.AG