Geodesic
Resultants and Chow forms via exterior syzygies
Eisenbud, David1 ; Schreyer, Frank-Olaf2 ; Weyman, Jerzy3
1 Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
2 Mathematik und Informatik, Geb. 27, Universität des Saarlandes, D-66123 Saarbrücken, Germany
3 Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
Journal of the American Mathematical Society, Tome 16 (2003) no. 3, pp. 537-579

Voir la notice de l'article provenant de la source American Mathematical Society

Given a sheaf on a projective space ${\mathbf P}^n$, we define a sequence of canonical and effectively computable Chow complexes on the Grassmannians of planes in ${\mathbf P}^n$, generalizing the well-known Beilinson monad on ${\mathbf P}^n$. If the sheaf has dimension $k$, then the Chow form of the associated $k$-cycle is the determinant of the Chow complex on the Grassmannian of planes of codimension $k+1$. Using the theory of vector bundles and the canonical nature of the complexes, we are able to give explicit determinantal and Pfaffian formulas for resultants in some cases where no polynomial formulas were known. For example, the Horrocks–Mumford bundle gives rise to a polynomial formula for the resultant of five homogeneous forms of degree eight in five variables.
DOI : 10.1090/S0894-0347-03-00423-5

Eisenbud, David 1 ; Schreyer, Frank-Olaf 2 ; Weyman, Jerzy 3

1 Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
2 Mathematik und Informatik, Geb. 27, Universität des Saarlandes, D-66123 Saarbrücken, Germany
3 Department of Mathematics, Northeastern University, Boston, Massachusetts 02115 
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Eisenbud, David; Schreyer, Frank-Olaf; Weyman, Jerzy. Resultants and Chow forms via exterior syzygies. Journal of the American Mathematical Society, Tome 16 (2003) no. 3, pp. 537-579. doi: 10.1090/S0894-0347-03-00423-5

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