JournalsrsmupVol. 136pp. 111–136

Q\mathbb Q-Gorenstein smoothings of surfaces and degenerations of curves

  • Giancarlo Urzúa

    Pontificia Universidad Católica de Chile, Santiago de Chile, Chile
$\mathbb Q$-Gorenstein smoothings of surfaces and degenerations of curves cover
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Abstract

In this paper we mainly describe Q\mathbb Q-Gorenstein smoothings of projective surfaces with only Wahl singularities which have birational fibers. For instance, these degenerations appear in normal degenerations of P2\mathbb P^2, 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 K2=1K^2=1, pg=0p_g=0, and π1=0\pi_1=0 using plane curves.

Cite this article

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

DOI 10.4171/RSMUP/136-9