2008/12/18 by Travis Kopp, Kopp, Travis · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Finite Group Theory Research #math.AG #msc:14E05 #msc:14J40 #msc:14J70
paper · pdf · doi:10.48550/arxiv.0812.3454
13 pages
arxiv created 2008/12/18 · arxiv updated 2009/12/01
This paper was inspired by work by T. Peternell, M. Schneider and A.J. Sommese on the Kodaira dimension of subvarieties. In it I find a relation between the Kodaira-Iitaka dimension of a divisor on a normal variety and that of related divisors on an irreducible normal subvariety of codimension one. The main result may be stated in a simplified form as: For X a complete normal variety, Y \sub X an irreducible complete normal divisor and \sL an invertible sheaf on X, there exist integers n1 > 0, n2 ≥ 0 for which κ(X,\sL) - 1 ≤ κ(Y,\sLn1(-n2Y)|Y), where, if Y is not a fixed component of large tensor powers of \sL, we may take n1 >> n2. This has implications for Kodaira-Iitaka dimension on a subvariety of any codimension.