Real varieties associated to complex varieties

✍ Scribed by E. Ballico

• Book ID: 104152687
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 109 KB
• Volume: 185
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(03)00108-7

✦ Synopsis

For any irreducible and reduced compact complex space or any integral projective variety, let X be its complex conjugate. Let S(X ) be the set of all W such that W × W ∼ = X × X . We say that S(X ) is trivial if for every W ∈ S(X ) there are Y; Z such that X ∼ = Y × Z and W ∼ = Y × Z . A torsion bundle over a torus is the total space of a ÿbre bundle with ÿnite structure group over a positive dimensional torus. Here we prove that if X has no torsion bundle over a torus as a factor, then S(X ) is trivial.