This thesis exhibits two of the author's works: the first is about interpreting the derived equivalences of K3 surfaces through Cremona transformations, where we construct a birational automorphism of projective fourfold with base loci birational to nontrivially derived equivalent K3 surfaces. The second is about the rationality problem of cubic fourfolds. We present two examples of cubic fourfolds which contain families of rational scrolls naturally arise from their Hodge structures. By exploiting the rational scrolls, we show that one example is rational and the other one admits unirational parametrizations of odd degree.
Lai, Kuan-Wen,
"Cremona transformations and rational parametrizations inspired by Hodge theory"
(2018).
Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.26300/yv4t-6v86
