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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)

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