On projective 3-folds of general type with small positive geometric genus

Abstract

In this paper we study pluricanonical maps of minimal projective 3-folds of general type with geometric genus $1$, $2$ and $3$. We go in the direction pioneered by Enriques and Bombieri, and other authors, pinning down, for low projective genus, a finite list of exceptions to the birationality of some pluricanonical map. In particular, apart from a finite list of weighted baskets, we prove the birationality of ${\phi }_{16}$, ${\phi }_6$ and ${\phi }_5$ respectively.

Final version, 36 pages. Electronic Research Archive (to appear)

References in corpus (1)

• Canonical stability in terms of singularity index for algebraic threefolds

Cited by in corpus (2)

• On projective threefolds of general type with p_g=2
• The Noether inequality for threefolds and three moduli spaces with minimal volumes