[Colloquium]Part I-Moduli and smooth specialization of hypersurfaces in a smooth projective variety

Date: Apr. 7(Fri)
Speaker: Yongnam Lee (IBS-CCG, KAIST)
Abstract:
In the first part of the colloquium talk, we will introduce some theories about construction of moduli space of hypersurfaces in the projective space. In the second part, we give a structure theorem for projective manifolds $W_0$ with the property of admitting a one parameter deformation where $W_t$ is a smooth hypersurface in a smooth projective variety $Z_t$. Their structure is the one of special iterated univariate coverings, which we call normal type. We give an application to the case where $Z_t$ is a projective space, respectively an abelian variety.
We also give a characterizaton of smooth ample hypersurfaces in abelian varieties and describe an irreducible connected component of their moduli space. The second part is based on joint work with Fabrizio Catanese.

#postechmathematics #mathematics #MathColloquium