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Transactions of the American Mathematical Society

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Calculating discriminants by higher direct images

Author: Jerzy Weyman
Journal: Trans. Amer. Math. Soc. 343 (1994), 367-389
MSC: Primary 14M12; Secondary 14F10
MathSciNet review: 1184118
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Abstract: The author uses the homological algebra to construct for any line bundle $ \mathcal{L}$ on a nonsingular projective variety X the complex $ \mathbb{F}(\mathcal{L})$ whose determinant is equal to the equation of the dual variety $ {X^{\text{V}}}$. This generalizes the Cayley-Koszul complexes defined by Gelfand, Kapranov and Zelevinski. The formulas for the codimension and degree of $ {X^{\text{V}}}$ in terms of complexes $ \mathbb{F}(\mathcal{L})$ are given. In the second part of the article the general technique is applied to classical discriminants and hyperdeterminants.

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