Please use this identifier to cite or link to this item: https://doi.org/10.1142/S0129167X09005534
Title: Effective Ljasiewicz inequality for arithmetically defined varieties and a geometric application to bihomogeneous polynomials
Authors: To, W.-K. 
Yeung, S.-K.
Keywords: Arithmetically defined varieties
Bihomogeneous polynomials
Lojasiewicz inequality
Issue Date: Jul-2009
Source: To, W.-K., Yeung, S.-K. (2009-07). Effective Ljasiewicz inequality for arithmetically defined varieties and a geometric application to bihomogeneous polynomials. International Journal of Mathematics 20 (7) : 915-944. ScholarBank@NUS Repository. https://doi.org/10.1142/S0129167X09005534
Abstract: We establish two versions of effective Lojasiewicz inequality for arithmetically defined affine varieties. As an application, we consider bihomogeneous polynomials on the complex Euclidean space which are positive along the affine cone of an arithmetically defined projective variety, and we obtain effective estimates on certain modifications needed to turn them into sums of squares of pointwise norms of homogeneous polynomials. The latter can be interpreted as an effective result on isometric embeddings for the associated indefinite Hermitian holomorphic line bundles. © 2009 World Scientific Publishing Company.
Source Title: International Journal of Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/103176
ISSN: 0129167X
DOI: 10.1142/S0129167X09005534
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