Infinitesimal Torelli Theorem for regular surfaces with very ample canonical divisor

TL;DR

This paper proves the Infinitesimal Torelli theorem for certain regular surfaces with ample, globally generated canonical bundles, high geometric genus, and zero irregularity, revealing new insights into their deformation theory.

Contribution

It introduces a novel realization of Kodaira-Spencer classes within the kernel of the cohomology cup-product, advancing understanding of the period map for these surfaces.

Findings

Infinitesimal Torelli theorem holds under specified conditions.

Kodaira-Spencer classes are realized in the kernel of the cup-product.

Enhanced understanding of the period map's derivative for these surfaces.

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 $p_g \geq 4$, 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.