Open Access
Translator Disclaimer
2006 Some Geometry and Combinatorics for the $S$-Invariant of Ternary Cubics
P. M. H. Wilson
Experiment. Math. 15(4): 479-490 (2006).


In earlier papers, P. M. H. Wilson, “Sectional Curvatures of Kähler Moduli,” and B. Totaro, “The Curvature of a Hessian Metric,” the $S$-invariant of a ternary cubic $f$ was interpreted in terms of the curvature of related Riemannian and pseudo-Riemannian metrics. This is clarified further in Section 3 of this paper. In the case that $f$ arises from the cubic form on the second cohomology of a smooth projective threefold with second Betti number three, the value of the $S$-invariant is closely linked to the behavior of this curvature on the open cone consisting of Kähler classes. In this paper, we concentrate on the cubic forms arising from complete intersection threefolds in the product of three projective spaces, and investigate various conjectures of a combinatorial nature arising from their invariants.


Download Citation

P. M. H. Wilson. "Some Geometry and Combinatorics for the $S$-Invariant of Ternary Cubics." Experiment. Math. 15 (4) 479 - 490, 2006.


Published: 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1172.14332
MathSciNet: MR2293598

Primary: 15A72
Secondary: 14H52 , 32J27 , 53A15

Keywords: combinatorial inequalities , curvature , invariant theory , Ternary cubics

Rights: Copyright © 2006 A K Peters, Ltd.


Vol.15 • No. 4 • 2006
Back to Top