Covers of algebraic varieties III. The discriminant of a cover of degree 4 and the trigonal construction

Casnati, G.

doi:10.1090/S0002-9947-98-02136-9

Covers of algebraic varieties III. The discriminant of a cover of degree 4 and the trigonal construction
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Trans. Amer. Math. Soc. 350 (1998), 1359-1378 Request permission

Abstract:

For each Gorenstein cover $\varrho \colon X\to Y$ of degree $4$ we define a scheme $\Delta (X)$ and a generically finite map $\Delta (\varrho )\colon \Delta (X)\to Y$ of degree $3$ called the discriminant of $\varrho$. Using this construction we deal with smooth degree $4$ covers $\varrho \colon X\to \mathbb {P}_{\mathbb {C}}^ {n}{\mathbb {C}}$ with $n\ge 5$. Moreover we also generalize the trigonal construction of S. Recillas.

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