Holey Segre Varieties

✍ Scribed by L. Bader; A. Cossidente; M.J. de Resmini

• Book ID: 102570087
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 274 KB
• Volume: 22
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.2001.0513

✦ Synopsis

Holey Segre varieties are introduced, which generalize classical Segre varieties and whose existence is suggested by the fact that any non-prime finite field contains proper subfields. More precisely, a holey Segre variety is the tensor product P G(n, q) ⊗ P G(m, q k ). An algebraic description of such an object is given and its structure is investigated.

Furthermore, special choices of the parameters are considered, in which cases a holey Segre variety admits a partition into classical Segre varieties. Also, some holey Segre varieties are isomorphic to non-canonical subgeometries embedded in suitable Segre varieties.