The difference $[L_1]-[L_2] $ of a pair of skew lines on a cubic threefold defines a vanishing
cycle on the cubic surface as the hyperplane section spanned by the two lines. By deforming …

For a smooth projective variety X of dimension 2n-1 over complex field, Zhao defined the
topological Abel-Jacobi map, which sends vanishing cycles on a smooth hyperplane section …

Topological Abel-Jacobi Map for Hypersurfaces in Complex Projective Four-Space Page 1
Topological Abel-Jacobi Map for Hypersurfaces in Complex Projective Four-Space Dissertation …

Let X be a complex submanifold of projective space. Schnell showed that the middle-
dimensional primitive cohomology of X is generated by tube classes, which arise from the …

(1) SymkC Ñ JpCq, pp1,..., pkq ÞÑω ÞÑ ÿ i ż pi p0 ω that integrates holomorphic 1-forms
along paths joining a fixed point p0 to pi. It is used to prove the Lefschetz p1, 1q-theorem …

Let X Ă PN be a smooth projective variety over C of dimension 2n 1. Let f: X Ñ Osm be the
universal family of smooth hyperplane sections of X, where Osm is the Zariski open subset of …

Lefschetz initially proved the Lefschetz (1, 1)-theorem in 1924 by taking a Lefschetz pencil of
hyperplane sections for a complex projective surface. Lefschetz's method would provide a …