Syzygies of Special Varieties

[403703] Weyman本研究的目的是研究随着载体束的坍缩而产生的变异。研究的几个部分与这些变种中最有趣的例子相对应。第一部分研究广义判别式和结果式的度、行列式和奇异性。将特别注意经典的判别式和结果式以及多维矩阵的超行列式——判别式。第二部分讨论经典李代数中幂零元共轭类的奇异性。这里的主要目标是证明首席研究员关于非正常轨道的猜想。第三部分是研究多根二元形式的变化。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。

9403703 Weyman The aim of this research is to study the varieties arising as the collapsing of vector bundles. Several parts of the research correspond to the most interesting examples of such varieties. The first part is to study degrees, determinantal expressions and singularities of generalized discriminants and resultants. Special attention will be paid to the classical discriminants and resultants as well as the hyperdeterminants- the discriminants of multidimensional matrices. The second part is concerned with singularities of conjugacy classes of nilpotent elements in classical Lie algebras. The main goal here is to prove the principal investigator's conjecture on non-normal orbits. The third part is to sutdy the varieties of binary forms with multiple roots. 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.