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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: G. Casnati
Journal: Trans. Amer. Math. Soc. 350 (1998), 1359-1378
MSC (1991): Primary 14E20, 14E22
MathSciNet review: 1467462
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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 $\varrho \colon X\to {{\mathbb P}^{n}_{\mathbb{C}}}$ with $n\ge 5$. Moreover we also generalize the trigonal construction of S. Recillas.


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Additional Information

G. Casnati
Affiliation: Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, via Belzoni 7, I–35131 Padova (Italy)
Email: casnati@galileo.math.unipd.it

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02136-9
PII: S 0002-9947(98)02136-9
Keywords: Cover, Gorenstein, discriminant
Received by editor(s): December 1, 1995
Additional Notes: This work was done in the framework of the AGE project, H.C.M. contract ERBCHRXCT 940557.
Article copyright: © Copyright 1998 American Mathematical Society