2019/08/19 by Lee, Yongnam, Luo, Yujie, Zhang, De-Qi
#14D05 #14E05 #14J45 #14J70 #14M22 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1908.06894
Let X be a very general hypersurface of degree d in the projective (n+1)-space with n ≥ 3, and f: X → Y a non-birational surjective morphism to a normal projective variety Y. We first prove that Y is a klt Fano variety if \rm deg f ≥ C for some constant C = C(n, d) depending only on n and d. Next we prove an optimal upper bound \rm deg f ≤ \rm deg X provided that Y is factorial, \rm deg f is prime and \rm deg f ≥ E(n) for some constant E(n) (with E(n) = n(n+1) when Y is smooth). As a corollary, we show that Y≅ \bf Pn under some conditions on Y and \rm deg f.