Chern slopes of simply connected complex surfaces of general type are dense in [2,3]. (English) Zbl 1346.14097

For a smooth minimal complex surface of general type, the Chern numbers satisfy the so-called Bogomolov-Miyaoka-Yau inequality: \(c_1^2\leq 3c_2\). Moreover, the equality can hold if and only if the universal cover of the surface is a ball in \(\mathbb{C}^2\). In this paper, the authors prove that for any number \(r\in [2,3]\), there are spin (resp. nonspin and minimal) simply connected complex surfaces of general type with \(c_1^2/c_2\) 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. A central ingredient in their construction is a new family of special arrangements of elliptic curves in the projective plane.
Reviewer: Xin Lu (Mainz)


14J25 Special surfaces
14J15 Moduli, classification: analytic theory; relations with modular forms
14J29 Surfaces of general type
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