Sectional Invariants of Hyperquadric Fibrations over a Smooth Projective Curve

Abstract

Let $(X,L)$ be a hyperquadric fibration over a smooth curve with $\dim X=n\geq 3$. In this paper we will calculate the $i$th sectional Euler number $e_i(X,L)$ of $(X,L)$. Using this, we will study a lower bound for the $i$th sectional Betti number $b_i(X,L)$ with $i\leq 4$. In particular we will prove that $b_2(X,L)\geq 3$, $b_3(X,L)\geq 0$ and $b_4(X,L)\geq 3$.