The determination of integral closures and geometric applications

Details The determination of integral closures and geometric applications The determination of integral closures and geometric applications

2003-10-30

arxiv.org/abs/math/0310467v2

Mathematics

Algebraic Geometry

Advances in Mathematics, to appear (no changes, just add this info)

Scientific paper

We express explicitly the integral closures of some ring extensions; this is done for all Bring-Jerrard extensions of any degree as well as for all general extensions of degree < 6; so far such an explicit expression is known only for degree < 4 extensions. As a geometric application we present explicitly the structure sheaf of every Bring-Jerrard covering space in terms of coefficients of the equation defining the covering; in particular, we show that a degree-3 morphism f : Y --> X is quasi-etale if and only if the first Chern class of the sheaf f_*(O_Y) is trivial (details in Theorem 5.3). We also try to get a geometric Galoisness criterion for an arbitrary degree-n finite morphism; this is successfully done when n = 3 and less satifactorily done when n = 5.

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