On webs of maximum rank

✍ Scribed by John B. Little

• Publisher: Springer
• Year: 1989
• Tongue: English
• Weight: 754 KB
• Volume: 31
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00184156

✦ Synopsis

This paper contains two results on webs of maximal rank. First, we show that at each point, the web normals for a codimension-r web of maximum r-rank are (r -1)-dimensional generators of a rational normal scroll in the projectivized tangent space to the web domain, an extension of a theorem of Chem. and Griffiths in the case r = 2 [5]. We use this statement to deduce that webs of maximum rank are almost-Grassmannizable in the sense of Akivis [1]. Second, we show that there are exceptional (that is, maximum rank, but not algebraizable) webs W(2n, n, 2) for all n >/2. The construction relies on the properties of zero-cycles on algebraic K3 surfaces.