Mathematics – Algebraic Geometry
Scientific paper
2012-02-13
Mathematics
Algebraic Geometry
13 pages, welcome comments
Scientific paper
For a smooth minimal surface of general type $S$ with $Albdim(S) = 2$, Severi inequality says that $K_S^2 \geq 4\chi(S)$, which was proved by Pardini. It is expected that when the equality is attained, $S$ is birational to a double cover over an Abelian surface branched along a divisor having at most negligible singularities. This was proved when $K_S$ is ample by Manetti. In this paper, we applied Manetti's method to the canonical model of $S$, with some additional assumptions we proved Severi inequality and characterized the surfaces with $K_S^2 = 4\chi(S)$.In addition, we gave a characterization of the double cover over an Abelian surface via the ramification divisor.
No associations
LandOfFree
An orbifold approach to Severi Inequality does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with An orbifold approach to Severi Inequality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An orbifold approach to Severi Inequality will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-681371