Topology of complete intersections

Abstract

Let Xn(d) and Xn(d') be two n-dimensional complete intersections with the same total degree d. In this paper we prove that, if n is even and d has no prime factors less than $\frac{n+3}{2}$ , then Xn(d) and Xn(d') are homotopy equivalent if and only if they have the same Euler characteristics and signatures. This confirms a conjecture of Libgober and Wood [16]. Furthermore, we prove that, if d has no prime factors less than $\frac{n+3}{2}$ , then Xn(d) and Xn(d') are homeomorphic if and only if their Pontryagin classes and Euler characteristics agree.