Rational configurations in K3 surfaces and simply-connected p_g=1 surfaces for K²=1,2,3,4,5,6,7,8,9

2021/10/20 by Reyes, Javier, Urzúa, Giancarlo · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2110.10629

Abstract

We prove the existence of (20-2K²)-dimensional families of simply-connected surfaces with ample canonical class, p_g=1, and 1 ≤ K² ≤ 9, and we study the relation with configurations of rational curves in K3 surfaces via \mathbb Q-Gorenstein smoothings. Our surfaces with K²=7 and K²=9 are the first surfaces known in the literature, together with the existence of a 4-dimensional family for K²=8.

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• Wahl singularities in degenerations of del Pezzo surfaces

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