On the geography of threefolds of general type

Abstract

Let X be a complex nonsingular projective 3-fold of general type. We show that there are positive constants c, c and m 1 such that χ (ω X ) −c Vol( X) and P m (X) c m 3 Vol( X) for all m m 1 .

Geography of Irregular Gorenstein 3–folds

“…For example, there do exist examples of non-Gorenstein 3-folds of maximal Albanese dimension with χ(ω X ) = 0 (see [15]). In [11], Chen and Hacon have constructed a family of non-Gorenstein 3-folds of general type with χ(ω X ) negative. In their paper, they obtained a similar type of inequality K 3 X ≥ cχ(ω X ) but c < 0.…”

Threefolds of Kodaira dimension one

“…There are six fixed points on F 3 , namely [1 : ω : ω 2 : 0], [1 : ω 2 : ω : 0] and [1 : 1 : 1 : u i ] i=1,..., 4 , where w = e We have…”