Complex Geometry of Iwasawa Manifolds

Student: Rogov Vasilii

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2018

Iwasawa manifold is a compact complex homogeneous manifold isomorphic to a quotient $G/\Lambda$, where $G$ is the group of complex unipotent $3 \times 3$-matrices and $\Lambda \subset G$ is a cocompact lattice. We prove that any compact complex curve in an Iwasawa manifold is contained in a holomorphic subtorus. We also prove that any complex surface in an Iwasawa manifold is either an abelian surface or a K \"ahler non-projective isotrivial elliptic surface of Kodaira dimension one. In the Appendix we show that any subtorus in Iwasawa manifold carries complex multiplication.

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