On the classification of product-quotient surfaces with $q=0$, pg=3 and their canonical map

In this work we present new results to produce an algorithm that returns, for any fixed pair of natural integers K² and χ, all regular surfaces S of general type with self-intersection KS²=K² and Euler characteristic χ( OS)=χ, that are product-quotient surfaces. The key result we obtain is an algebraic characterization of all families of regular product-quotients surfaces, up to isomorphism, arising from a pair of G-coverings of P¹. As a consequence of our work, we provide a classification of all regular product-quotient surfaces of general type with 23≤ K²≤ 32 and χ( OS)=4. Furthermore, we study their canonical map and present several new examples of surfaces of general type with a high degree of the canonical map.