-Gorenstein smoothings of surfaces and degenerations of curves
Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 111-136.

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 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 K 2 =1, p g =0, and π 1 =0 using plane curves.

DOI : 10.4171/RSMUP/136-9
Classification : 14
Mots clés : Surfaces of general type, moduli spaces, minimal model program, $\mathbb Q$-Gorenstein smoothings
Urzúa, Giancarlo 1

1 Pontificia Universidad Católica de Chile, SANTIAGO DE CHILE, CHILE
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     title = {$\mathbb Q${-Gorenstein} smoothings of surfaces and degenerations of curves},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {111--136},
     publisher = {European Mathematical Society Publishing House},
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Urzúa, Giancarlo. $\mathbb Q$-Gorenstein smoothings of surfaces and degenerations of curves. Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 111-136. doi : 10.4171/RSMUP/136-9. http://www.numdam.org/articles/10.4171/RSMUP/136-9/

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