paper

On birational trivial families and Adjoint quadrics

arXiv:1903.06307

Abstract

Let $I ¨ : X \to B$ be a family whose general fiber $X_{b}$ gives a $(d_{1}, ..., d_{a})$ polarisation of a general Abelian variety where $1 \leq d_{i} \leq 2$ , $i = 1, ..., a$ and $a \geq 4$ . We show that the fibers are in the same birational class if all the $(m, 0)$ forms on $X_{b}$ are liftable to $(m, 0)$ forms on $X$ where $m = 1$ and $m = a - 1$ . Actually we show general criteria to find families with fibers in the same birational class, which leads together with a famous theorem of Nori to some interesting applications.

18 pages