发表机构
Purdue University（普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对由至多c项多项式生成的理想及toric理想，给出了正则性关于重数的上界，分别小于三重指数和双重指数，改进了Eisenbud-Goto猜想的否定结果。
AI 中文摘要
Eisenbud-Goto猜想指出，在代数闭域上的多项式环中，齐次素理想的Castelnuovo-Mumford正则性以重数减高度加一为上界。2017年，McCullough和Peeva证明了任意齐次素理想的正则性不能被重数的任何多项式函数所界定。对于由至多$c$项多项式生成的理想，我们给出了一个正则性的界，该界小于$c$和重数的三重指数。此外，对于toric理想，我们得到了一个关于重数的小于双重指数的界。
英文摘要
The Eisenbud-Goto conjecture stated that for a homogeneous prime ideal in a polynomial ring over an algebraically closed field, the Castelnuovo-Mumford regularity is bounded above by the multiplicity minus height plus one. In 2017, McCullough and Peeva showed that the regularity of an arbitrary homogeneous prime cannot be bounded by any polynomial function of the multiplicity. For ideals generated by polynomials with at most $c$ terms, we present a bound on the regularity which is less than triple exponential in $c$ and the multiplicity. Furthermore, for toric ideals we get a bound that is smaller than double exponential in terms of multiplicity.
