Incident rational curves
arXiv:2006.14589 · doi:10.1007/s40879-020-00407-y
Abstract
We study families of rational curves on an algebraic variety satisfying incidence conditions. We prove an analogue of bend-and-break: that is, we show that under suitable conditions, such a family must contain reducibles. In the case of curves in incident to certain complete intersections, we prove the family is irreducible.