Please use this identifier to cite or link to this item: https://doi.org/10.1112/S0024610706022708
Title: Effective isometric embeddings for certain Hermitian holomorphic line bundles
Authors: To, W.-K. 
Yeung, S.-K.
Issue Date: Jun-2006
Source: To, W.-K., Yeung, S.-K. (2006-06). Effective isometric embeddings for certain Hermitian holomorphic line bundles. Journal of the London Mathematical Society 73 (3) : 607-624. ScholarBank@NUS Repository. https://doi.org/10.1112/S0024610706022708
Abstract: We consider bihomogeneous polynomials on complex Euclidean spaces that are positive outside the origin and obtain effective estimates on certain modifications needed to turn them into squares of norms of vector-valued polynomials on complex Euclidean space. The corresponding results for hypersurfaces in complex Euclidean spaces are also proved. The results can be considered as Hermitian analogues of Hilbert's seventeenth problem on representing a positive definite quadratic form on ℝn as a sum of squares of rational functions. They can also be regarded as effective estimates on the power of a Hermitian line bundle required for isometric projective embedding. Further applications are discussed. © 2006 London Mathematical Society.
Source Title: Journal of the London Mathematical Society
URI: http://scholarbank.nus.edu.sg/handle/10635/103175
ISSN: 00246107
DOI: 10.1112/S0024610706022708
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