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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Covers of algebraic varieties III. The discriminant of a cover of degree 4 and the trigonal construction
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by G. Casnati PDF
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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Additional Information
  • G. Casnati
  • Affiliation: Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, via Belzoni 7, I–35131 Padova (Italy)
  • MR Author ID: 313798
  • Email: casnati@galileo.math.unipd.it
  • 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.
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 1359-1378
  • MSC (1991): Primary 14E20, 14E22
  • DOI: https://doi.org/10.1090/S0002-9947-98-02136-9
  • MathSciNet review: 1467462