{
"id": "1810.04662",
"version": "v1",
"published": "2018-10-10T17:49:11.000Z",
"updated": "2018-10-10T17:49:11.000Z",
"title": "Hodge-index type inequalities, hyperbolic polynomials and complex Hessian equations",
"authors": [
"Jian Xiao"
],
"categories": [
"math.AG",
"math.CV"
],
"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 G{\\aa}rding'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.",
"revisions": [
{
"version": "v1",
"updated": "2018-10-10T17:49:11.000Z"
}
],
"analyses": {
"keywords": [
"complex hessian equations",
"hodge-index type inequalities",
"hyperbolic polynomials",
"hodge-index type theorem holds",
"elementary symmetric polynomials implies"
],
"note": {
"typesetting": "TeX",
"pages": 0,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}