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

Xavier Roulleau (1) , Giancarlo Urzúa (2)

1 UP - Université de Poitiers = University of Poitiers
2 UC - Pontificia Universidad Católica de Chile

We prove that for any number r∈[2,3], there are spin (resp. nonspin and minimal) simply connected complex surfaces of general type X with c21(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 c21(X)/c2(X) arbitrarily close to r and π1(X) isomorphic to the fundamental group of a compact Riemann surface of genus q. %A central ingredient is a new family of special arrangements of elliptic curves in the projective plane.

Mots clés: Arrangements of curves; Geography; Simply connected complex surfaces; Spin 4-manifolds; Surfaces of general type

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]

Xavier Roulleau, Giancarlo Urzúa. Chern slopes of simply connected complex surfaces of general type are dense in [2,3]. 2024. ⟨hal-02112712⟩