Seminar Fellowship of the Ring - Jinhyung Park (KAIST) скачать в хорошем качестве

Seminar Fellowship of the Ring - Jinhyung Park (KAIST)

Title: Singularities and syzygies of secant varieties of smooth projective varieties Abstract: Given a smooth projective variety embedded in projective space, the k-th secant variety is the Zariski closure of the union of the linear spans of k+1 points. Assuming the embedding is complete and sufficiently positive, we expect that secant varieties exhibit nice uniform behavior. When the given variety is a curve or a surface, we show that the k-th secant variety has normal Du Bois singularities and the minimal free resolution of its section ring is as simple as possible for the first few steps. Furthermore, we also prove that the ideal of the k-th secant variety is determinantally presented. This is joint work with Doyoung Choi, Justin Lacini, and John Sheridan, as well as with Daniele Agostini.