Authors: Bin Wang
We discuss a structure that exists in many problems on smooth projective varieties over the field of complex numbers, and name it as ``Algebraic Poincar\'e duality" or ``APD" for abbreviation. In particular, over the complex numbers with singular cohomology, it is a solution to (1) Griffiths' conjecture on the incidence equivalence versus Abel-Jacobi equivalence, (2) Generalized Hodge conjecture of level 1, (3) Generalized Hodge conjecture of level 0, i.e. the usual Hodge conjecture, (4) The standard conjectures, (5) Grothendieck's ``D" conjecture. However it is not the goal of this paper to show APD implies these conjectures. In this paper we'll build the foundation for the structure by introducing the APD in its simplest form over the complex numbers.
Comments: 20 Pages. This is the first of three papers, all of which are posted on this site.
[v1] 2016-05-30 15:49:46
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