4 papers
Effective results on projective normality of the first and second secant varieties
Doyoung Choi, Jinhyung Park
In joint work with Lacini and Sheridan, we proved that the first and second secant varieties of a smooth projective complex variety embedded by the complete linear system of a suff…
Hilbert polynomials of the first and second secant varieties
Doyoung Choi, Jinhyung Park
In this paper, we give a description of the cohomology groups of the symmetric powers of the tautological bundle associated with a sufficiently positive line bundle on the Hilbert…
Singularities of the nested Hilbert scheme of points of length 3, 4
Doyoung Choi
We show that the projection morphism $X^{[3,4]} \lra X^{[3]}$ is flat even if it has reducible fiber. After analyzing blow-up constructions related to , we conclude that…
Singularities and syzygies of secant varieties of smooth projective varieties
Doyoung Choi, Justin Lacini, Jinhyung Park +1
We study the higher secant varieties of a smooth projective variety embedded in projective space. We prove that when the variety is a surface and the embedding line bundle is suffi…