2003/11/12 by Ichiro Shimada, Shimada, Ichiro
Computer Science · Mathematics · #14C30 #14M10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14C30 #msc:14M10
paper · pdf · doi:10.48550/arxiv.math/0311180
30pages, 2 figures
arxiv created 2003/11/12 · openalex publication_date 2003/11/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a general complete intersection of a given multi-degree in a complex projective space. Suppose that the anti-canonical line bundle of X is ample. Using the cylinder homomorphism associated with the family of complete intersections contained in X, we prove that the vanishing cycles in the middle homology group of X are represented by topological cycles whose support is contained in a proper Zariski closed subset T⊂ X of certain codimension. In some cases, we can find such a Zariski closed subset T with codimension equal to the upper bound obtained from the Hodge structure of the middle cohomology group of X by means of Gröbner bases. Hence a consequence of the generalized Hodge conjecture is verified in these cases.