The Cayley-Bacharach Condition
A set of points S in n-dimensional projective space is said to satisfy the Cayley-Bacharach condition with respect to degree r polynomials, or is CB(r), if any degree r homogeneous polynomial vanishing on all but one point of S must vanish at the final point. In recent literature, the condition has played an important role in computing a birational invariant called the degree of irrationality. However, the condition itself has not been studied extensively, and surprisingly little is known about the behavior of CB(r) points. We will discuss a new approach to studying the CB(r) condition, using combinatorial methods from matroid theory, and present some results to demonstrate how matroid theory can help us understand this condition in greater depth.
Advisor: Brooke Ullery.
Event Type: Dissertation. Research Area: Defense. Location: MSC E406. Speaker Name: Rohan Nair. Speaker Institution: Emory University.
Wednesday, June 25, 2025, 9:00 AM – 10:30 AM.