Quartic Rings Associated to Binary Quartic Forms

@article{Wood2012QuarticRA,
  title={Quartic Rings Associated to Binary Quartic Forms},
  author={M. Wood},
  journal={International Mathematics Research Notices},
  year={2012},
  volume={2012},
  pages={1300-1320}
}
  • M. Wood
  • Published 2012
  • Mathematics
  • International Mathematics Research Notices
  • We give a bijection between binary quartic forms and quartic rings with a monogenic cubic resolvent ring, relating the rings associated to binary quartic forms with Bhargava’s cubic resolvent rings. This gives a parametrization of quartic rings with monogenic cubic resolvents. We also give a geometric interpretation of this parametrization. 
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    References

    SHOWING 1-10 OF 26 REFERENCES
    Parametrizing quartic algebras over an arbitrary base
    • 14
    • PDF
    Composition of binary quadratic forms
    • 27
    Gauss composition over an arbitrary base
    • 20
    • PDF
    Rings and ideals parameterized by binary n-ic forms
    • M. Wood
    • Mathematics, Computer Science
    • J. Lond. Math. Soc.
    • 2011
    • 24
    • Highly Influential
    • PDF
    Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves
    • 125
    • Highly Influential
    • PDF
    The index of nonmonic polynomials
    • 15
    On the computation of quadratic 2-class groups
    • 24
    • PDF
    Rational Quadratic Forms
    • 453
    Introduction to Number Theory
    • 75
    • PDF