Calculating discriminants by higher direct images

Weyman, Jerzy

doi:10.1090/S0002-9947-1994-1184118-6

Calculating discriminants by higher direct images
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by Jerzy Weyman

Trans. Amer. Math. Soc. 343 (1994), 367-389

DOI: https://doi.org/10.1090/S0002-9947-1994-1184118-6

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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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