Mathematical Sciences: Complex Manifolds and Meromorphic Mappings

这个项目继续数学研究的问题 与多复变函数理论有关。 它将集中在亚纯函数的分离解析性问题上， 功能协调发展的 虽然Hartog定理说明了分离 解析性意味着定义在 域，一个不能作出如此广泛的声明，如果单独的 解析性仅限于较小的集合。 目前的工作寻求 扩展最近的结果限制解析 射影代数流形到 映射到紧致Kahler流形。 第二条调查路线涉及度的界限 在解决多项式方程。 如果一个理想是由 有限次数的多项式，理想中的多项式可以是 表示为生成元的乘积的组合（与 其他多项式）。 乘法器的最小度数不是 已知的，虽然尖锐的结果可以得到，如果轨迹的 可以测量发电机的根。 工作将继续在 在限制较少的情况下， 假设 //

This project continues mathematical research on problems related to the theory of functions of several complex variables. It will focus on the issue of separate analyticity of meromorphic functions. Although Hartog's theorem illustrates that separate analyticity implies joint analyticity for functions defined in domains, one cannnot make such broad statements if the separate analyticity is confined to smaller sets. The present work seeks to expand recent results on restricted analyticity of meromorphic mappings of projective algebraic manifolds to mappings into compact Kahler manifolds. A second line of investigation concerns bounds for degrees in solving polynomial equations. If an ideal is generated by polynomials of limited degree, a polynomial in the ideal may be expressed as combinations of products of the generators (with other polynomials). The minimal degree of the multipliers is not known, although sharp results can be obtained if the locus of roots of the generators can be measured. Work will continue in an effort to improve the bounds under less restrictive hypotheses. //