Birational isomorphisms of four-dimensional quintics.
Birational positivity in dimension
In this paper we prove that for a nonsingular projective variety of dimension at most 4 and with non-negative Kodaira dimension, the Kodaira dimension of coherent subsheaves of is bounded from above by the Kodaira dimension of the variety. This implies the finiteness of the fundamental group for such an provided that has vanishing Kodaira dimension and non-trivial holomorphic Euler characteristic.
Boundedness for codimension two submanifolds of quadrics.
It is proved that there are only finitely many families of codimension two subvarieties not of general type in Q6.