Inequalities of Noether type for 3-folds of general type

2001/10/01 by Meng Chen, Chen, Meng
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds #math.AG #msc:14E05

paper · pdf · doi:10.48550/arxiv.math/0110012

25 pages, the final version, to appear in "Journal of the Mathematical Society of Japan"

arxiv created 2003/09/16 · arxiv updated 2009/11/30

Abstract

If X is a smooth complex projective 3-fold with ample canonical divisor K, then the inequality K³≥ 2/3(2p_g-7) holds, where p_g denotes the geometric genus. This inequality is nearly sharp. We also give similar, but more complicated, inequalities for general minimal 3-folds of general type. (A noether type of inequality lies, by all means, on the other side of the Miyaoka-Yau inequality from the geographical point of view.)

Related

• The Noether inequality for Gorenstein minimal 3-folds
• Algebraic threefolds of general type with small volume
• The Noether inequality for threefolds and three moduli spaces with minimal volumes
• Noether inequality for irregular threefolds of general type
• Noether-Severi inequality and equality for irregular threefolds of general type