Threefolds of P^5 with one apparent quadruple point

Hurwitz spaces of quadruple coverings of elliptic curves and the moduli space of abelian threefolds A_3(1,1,4)

We prove that the moduli space A_3(1,1,4) of polarized abelian threefolds with polarization of type (1,1,4) is unirational. By a result of Birkenhake and Lange this implies the unirationality of the isomorphic moduli space A_3(1,4,4). The result is based on the study the Hurwitz space H_{4,n}(Y) of quadruple coverings of an elliptic curve Y simply branched in n points. We prove the unirationality of its codimension one subvariety H^{0}_{4,A}(Y) which parametrizes quadruple coverings π:X --> Y with Tschirnhausen modules isomorphic to A^{-1}, where A\in Pic^{n/2}Y, and for which π^*:J(Y)--> J(X)…

Threefolds with one apparent double point

The number of apparent double points of an irreducible projective variety $X$ of dimension $n$ in $\mathbb{P}^{2n+1}$ is the number of secant lines to $X$ passing through a general point of $\mathbb{P}^{2n+1}$. This classical notion dates back to Severi. Smooth threefolds having one apparent double point (shortly OADP threefolds) have been classified in 2004 by Ciliberto, Mella and Russo. In 2011, Ciliberto and Russo have classified normal OADP threefolds such that the so-called fundamental surface is a plane. In this thesis the case in which the fundamental surface is not a plane is considere…

关于三重形上秩为一的叶形的Log Canonical极小模型程序

Log Canonical Minimal Model Program for corank one foliations on Threefolds

本文研究了三重形上秩为一的叶形的Log Canonical极小模型程序，证明了通过运行$(K_\mcF+\Delta)$-MMP可以得到极小模型或Mori纤维空间，并探讨了极小模型之间的连接及有限数量性质。