Algebraic Geometry. – On the classification of product-quotient surfaces with q D 0, pg D 3 and their canonical map

– In this work, we present new results to produce an algorithm that returns, for any fixed pair of positive integers K2 and, all regular surfaces S of general type with self-intersection of the canonical class KS2 D K2 and Euler characteristic .OS/ D, which 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 S of general type with 23 ≤ KS2 ≤ 32 and .OS/ D 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.