New explicit constructions of surfaces of general type

Key Points

• To construct smooth surfaces of general type and find new fake projective planes using these constructions.
• Constructed a four-dimensional family of smooth surfaces of general type.
• Utilized degeneration techniques to derive equations for new fake projective planes.
• Applied nontrivial computer calculations to support findings.
• Identified new explicit equations for six pairs of fake projective planes.
• Demonstrated that K_S^2 equals 3 for the constructed surfaces.
• Established the cyclic fundamental group C_{14} for the new surfaces.