Hodge-Index Type Inequalities, Hyperbolic Polynomials, and Complex Hessian Equations
Keyword(s):
Abstract It is noted that using complex Hessian equations and the concavity inequalities for elementary symmetric polynomials implies a generalized form of Hodge index inequality. Inspired by this result, using Gårding’s theory for hyperbolic polynomials, we obtain a mixed Hodge-index type theorem for classes of type $(1,1)$. The new feature is that this Hodge-index type theorem holds with respect to mixed polarizations in which some satisfy particular positivity condition but could be degenerate and even negative along some directions.
1982 ◽
Vol 59
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pp. 355-359
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2006 ◽
Vol 204
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pp. 619-646
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1974 ◽
Vol 8
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pp. 273-280
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2017 ◽
Vol 39
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pp. 389-399
2006 ◽
Vol 42
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pp. 523-549
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