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The integral closure of a trinomial extension and its application
谢大军 博士(复旦大学)
2018-01-01 12:13  华东师范大学

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摘要: Let $R$ be a Noetherian unique factorization domain such that $n$ and
$n-k$ are units, and let
$A=R[\alpha]$ be a finite extension over $R$ by adding a root of $\alpha$ of
an irreducible trinomial
$p(z)=z^n+sz^k+t$ over $R$. We will compute explicitly the integral closure
of $A$ in its fraction
field. We also determine the ramification divisor. As a geometric
application, we study the covering defining
by the equation $p(z)$, we present explicitly the structure sheaf of in
terms of coefficients of
the equation defining the covering.