SURFACES OF GENERAL TYPE WITH p_g= 1 AND q = 0

Abstract

Abstract. We construct a new family of simply connected minimal complex surfaces of general type with pg = 1, q = 0, and K 2 = 3, 4, 5, 6, 8 using a Q-Gorenstein smoothing theory.

Surfaces of general type with pg=1, q=0, K2=6 and grassmannians

“…The surface S that we have constructed is not a Todorov surface, neither one constructed by Park-Park-Shin in [PPS13]. Indeed the latter are simply connected, while for the former one can check that S is not contained in one of the 11 non empty irreducible families listed in [Mo88, pg 335].…”

Spherical subcategories in algebraic geometry

“…[4] for these notions and the following list. For Kynev surfaces, see [17] or [22]. We treat structure sheaves of ruled surfaces over elliptic curves in Example 5.8, and 2-spherelike structure sheaves in Proposition 5.5…”

Construction of surfaces of general type from elliptic surfaces via $${\mathbb{Q}}$$ -Gorenstein smoothing

“…By using the double covering E(2) → E(1), together with the methods developed in [15], one can produce simply connected minimal surfaces of general type with p g = 1 and q = 0. For example, such surfaces with 1 ≤ K 2 ≤ 6 are constructed in [22]. 3.…”