Studies In Commutative Algebra & Algebraic Geometry

9401428 Hochster该奖项支持交换代数和代数几何的研究。主要研究者将继续研究诺etherian环理论中几个长期存在的问题，探索这些问题与新兴的紧闭理论的关系，包括它与绝对积分闭包的关系，并更好地理解环上所有理想都紧闭的条件的几何意义。该助教将研究理想的初等分解、紧闭、混合多重、联合约简和局部环参数系统中单项式产生的理想。本研究涉及交换代数和代数几何中的若干问题。代数几何研究多项式方程族的解。人们既可以研究解集的几何，也可以通过研究解集上的某些函数来代数地解决问题，这些函数形成了所谓的交换环。这种对偶视角在交换代数和代数几何之间建立了紧密的联系。* * *

9401428 Hochster This award supports research in commutative algebra and algebraic geometry. The principle investigator will continue investigating several long standing questions in the theory of Noetherian rings, to explore the relationship of these questions with the burgeoning theory of tight closure, including its relationship to absolute integral closures and to achieve a better understanding of the geometric significance of the condition on a ring that all of its ideals be tightly closed. The faculty associate will study primary decompositions of ideals, tight closure, mixed multiplicities, joint reductions and ideals generated by monomials in a system of parameters in a local ring. This research is concerned with a number of questions in commutative algebra and algebraic geometry. Algebraic geometry studies solutions of families of polynomial equations. One can either study the geometry of the solution set or approach problems algebraically by investigating certain functions on the solution set that form what is called a commutative ring. This dual perspective creates a close connection between commutative algebra and algebraic geometry. ***