ON 4-FOLD COVERS OF ALGEBRAIC SURFACES

In 1975 Horikawa introduced a method of resolving singularities of double covers over a smooth surface, called the canonical resolution. Ashikaga gave a similar method for certain triple covers in 1992, and Tan constructed the canonical resolution for any triple covers in 2002. These methods are useful for the global or local study of branched covers of surfaces. In this paper, we consider similar resolution for 4-fold covers over a smooth surface, which is based on Lagrange’s method to solve quartic equations. By using this method, we compute the Chern numbers c21 and c2 of certain 4-fold covers over a smooth projective surface.