On the topological decomposition of the hypersurfaces in projective toric manifolds

2011/12/07 by Wei Wang, Wang, Wei
Mathematics · #57R19 #57R65 #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1112.1555

openalex publication_date 2011/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we want to discuss the topology of the non-singular hypersurface Yⁿ with complex dimension n in a projective toric manifold Xⁿ⁺¹. When n is odd, our main results are a decomposition of Yⁿ≅ Y'\sharp s(Sⁿ × Sⁿ) as a connected sum of s copies of Sⁿ × Sⁿ with a differential manifold Y' such that b_n (Y')=0 or 2. When n is even and the degree of Y in X is big enough, we find that Y also admits such a decomposition Y'\sharp s(Sⁿ × Sⁿ), where Y' satisfy b_n(Y')-|sign(Y')|=b_n(X)± sign(Hⁿ(X)), where sign(Hⁿ(X)) is the signature of a certain bilinear form defined on Hⁿ(X,\mz).

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