On threefolds with K³=2p_g−6

Abstract

It is known that if X is an n-dimensional normal variety, and D a nef and big Cartier divisor on it such that the associated map φ_D is generically finite then Dⁿ≥2(h⁰(X, \mathcal{O}_X(D))−n). We study the case in which the equality holds for n=3 and D=K_X is the canonical divisor.
We also produce a bound for the admissible degree of the canonical map of a threefold, when it is supposed to be generically finite.