论文标题
有限的草个割裂品种
Restricted Secant Varieties of Grassmannians
论文作者
论文摘要
有限的草个割草机品种是由对应于$ k $ planes的积分建造的，其交叉路口具有规定的维度。我们研究了被限制的司法割草机的维度，并通过发病率的构造将它们与草个割法的类似问题联系起来。我们定义了一个预期维度的概念，并为所有受限的草个割草机的尺寸提供了一个公式，如果baur-draisma-degraaf猜想是对司法的非缺陷性的，那是真的。我们还演示了Macaulay2中的示例计算，并指出使这些计算更有效的方法。我们还展示了编码理论的潜在应用。
Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to $k$-planes with the restriction that their intersection has a prescribed dimension. We study dimensions of restricted secant of Grassmannians and relate them to the analogous question for secants of Grassmannians via an incidence variety construction. We define a notion of expected dimension and give a formula for the dimension of all restricted secant varieties of Grassmannians that holds if the Baur-Draisma-deGraaf Conjecture on non-defectivity of Grassmannians is true. We also demonstrate example calculations in Macaulay2, and point out ways to make these calculations more efficient. We also show a potential application to coding theory.
