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.
Mots-clés : Surfaces of general type, moduli spaces, minimal model program, $\mathbb Q$-Gorenstein smoothings
Urzúa, Giancarlo 1
@article{RSMUP_2016__136__111_0,
author = {Urz\'ua, Giancarlo},
title = {$\mathbb Q${-Gorenstein} smoothings of surfaces and degenerations of curves},
journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
pages = {111--136},
year = {2016},
publisher = {European Mathematical Society Publishing House},
address = {Zuerich, Switzerland},
volume = {136},
doi = {10.4171/RSMUP/136-9},
url = {http://geodesic.mathdoc.fr/articles/10.4171/RSMUP/136-9/}
}
TY - JOUR AU - Urzúa, Giancarlo TI - $\mathbb Q$-Gorenstein smoothings of surfaces and degenerations of curves JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2016 SP - 111 EP - 136 VL - 136 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://geodesic.mathdoc.fr/articles/10.4171/RSMUP/136-9/ DO - 10.4171/RSMUP/136-9 ID - RSMUP_2016__136__111_0 ER -
%0 Journal Article %A Urzúa, Giancarlo %T $\mathbb Q$-Gorenstein smoothings of surfaces and degenerations of curves %J Rendiconti del Seminario Matematico della Università di Padova %D 2016 %P 111-136 %V 136 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://geodesic.mathdoc.fr/articles/10.4171/RSMUP/136-9/ %R 10.4171/RSMUP/136-9 %F RSMUP_2016__136__111_0
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
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