Mathematical Sciences: Complex Manifolds and Meromorphic Mappings

该项目继续对与多复变函数理论相关的问题进行数学研究。重点讨论亚纯函数的分离解析性问题。虽然Hartog定理说明了分离分析性意味着在域中定义的函数的联合分析性，但如果分离分析性仅限于较小的集合，则不能作出如此广泛的陈述。目前的工作旨在将最近关于射影代数流形的亚纯映射的限制解析性的结果扩展到映射到紧的Kahler流形。第二项研究涉及到解多项式方程时的度的界。如果理想是由有限次多项式生成的，则理想中的多项式可以表示为生成多项式的乘积的组合（与其他多项式）。乘数的最小度是不知道的，虽然如果可以测量发生器的根的轨迹，可以得到明显的结果。我们将继续努力改进限制较少的假设下的边界。//

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. //