Infinitesimal Torelli Theorem for regular surfaces with very ample canonical divisor

Abstract

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 $p_g\ge 4$, 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.

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