Chern slopes of simply connected complex surfaces of general type are dense in [2,3]

2014/02/24 by Xavier Roulleau, Giancarlo Urzúa, Roulleau, Xavier +1 · 1 citation
Mathematics · #14J29 #Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.AG #math.SG #msc:14J29

paper · pdf · doi:10.48550/arxiv.1402.5801

20 pages. Final version

arxiv created 2014/11/09 · arxiv updated 2014/11/11

Abstract

We prove that for any number r in [2,3], there are spin (resp. non-spin minimal) simply connected complex surfaces of general type X with c₁²(X)/c₂(X) arbitrarily close to r. In particular, this shows the existence of simply connected surfaces of general type arbitrarily close to the Bogomolov-Miyaoka-Yau line. In addition, we prove that for any r ∈ [1,3] and any integer q≥ 0, there are minimal complex surfaces of general type X with c₁²(X)/c₂(X) arbitrarily close to r, and π₁(X) isomorphic to the fundamental group of a compact Riemann surface of genus q.

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