Integrated study on problems related to branched Galois covers

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1. Construction problem of Galois covers : Galois covers for *_4 and *_4 have been studied by the head investigator. In 1999, he made investigation on such Galois covers based on the Lagrange's method in solving quartic equations. The idea was to understand the Langranges method in terms of linear equivalence of divisors on algebraic varieties. In the first half of 2000, he polished the results in 1999, and made them into more "user-friendly" form. All of these results and their applications are written in his preprint "Galois covers for *_4 and *_4 and their applications, which is submitted to Osaka Math.J.In the second half of 2000, he has started investigation about versal Galois covers. It gaves new daylight in the study of Galois covers with other kinds of finite groups such as *_5.2. Topology of open algebraic varieties : Some new examples of Zariski pairs were found by Tokunaga. Oka made the intensive study on (2, 3) torus sextic curve and the topology of their complement. Shimada gave a new invariant for the fundamental group of the complement to plane curves and applied it to study the Zariski pari given by Namba and Tsuchihashi.3. Singularites : Oka and his PhD Student Pho Duc Tai figured out almost all possible configurations of singularites of non-tame (2, 3) torus sextic curves.4. The fundamental study for Galois covers : Kurano and Ogoma gave some new results in commutative algebra. Tsuchimoto studied non-commutative algebraic geometry.