-Gorenstein smoothings of surfaces and degenerations of curves

  • Giancarlo Urzúa

    Pontificia Universidad Católica de Chile, Santiago de Chile, Chile

Abstract

In this paper we mainly describe -Gorenstein smoothings of projective surfaces with only Wahl singularities which have birational fibers. For instance, these degenerations appear in normal degenerations of , and in boundary divisors of the KSBA compactification of the moduli space of surfaces of general type [15]. We give an explicit description of them as smooth deformations plus 3-fold birational operations, through the flips and divisorial contractions in [9]. We interpret the continuous part (smooth deformations) as degenerations of certain curves in the general fiber. At the end, we work out examples happening in the KSBA boundary for invariants , , and using plane curves.

Cite this article

Giancarlo Urzúa, -Gorenstein smoothings of surfaces and degenerations of curves. Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 111–136

DOI 10.4171/RSMUP/136-9