A set of points Z in $\mathbb{P}^3$ is an (a, b)-geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point to a plane is a complete intersection of curves of degrees a and b. We will report on some results in order to pursue classification of geproci sets. Specifically, we will show how to classify (a, b)-geproci sets Z which consist of a points on each of b skew lines, assuming the skew lines have two transversals in common. We will show in this case that b ≤ 6. Moreover we will show that all geproci sets of this type and with no points on the transversals are contained in the $F_4$ configuration. We conjecture that a similar result is true for an arbitrary number a of points on each skew line, replacing containment in $F_4$ by containment in a half grid obtained by the so-called standard construction.

https://zoom.us/join
Meeting ID: 9086116889
Passcode: 362880
Email: agnt@ipm.ir