An orbifold approach to Severi Inequality

2012/02/13 by Zhang, Lei
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1202.2656

Abstract

For a smooth minimal surface of general type S with Albdim(S) = 2, Severi inequality says that K_S² ≥ 4χ(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_S² = 4χ(S).In addition, we gave a characterization of the double cover over an Abelian surface via the ramification divisor.

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