45 research outputs found
KSBA compactification of the moduli space of K3 surfaces with purely non-symplectic automorphism of order four
We describe a compactification by KSBA stable pairs of the five-dimensional
moduli space of K3 surfaces with purely non-symplectic automorphism of order
four and lattice polarization. These K3 surfaces can
be realized as the minimal resolution of the double cover of
branched along a specific curve. We
show that, up to a finite group action, this stable pairs compactification is
isomorphic to Kirwan's partial desingularization of the GIT quotient
with the symmetric linearization.Comment: 26 pages, 6 figures. We explain the connection with Alexeev-Thompson
work on ADE surfaces. Comments are welcom
Birational geometry of the moduli space of rank 2 parabolic vector bundles on a rational curve
We investigate the birational geometry (in the sense of Mori's program) of
the moduli space of rank 2 semistable parabolic vector bundles on a rational
curve. We compute the effective cone of the moduli space and show that all
birational models obtained by Mori's program are also moduli spaces of
parabolic vector bundles with certain parabolic weights.Comment: 22 pages, Revised, Published version in International Mathematics
Research Notices (2015
Moduli spaces of weighted pointed stable rational curves via GIT
We construct the Mumford-Knudsen space of n pointed stable rational curves by
a sequence of explicit blow-ups from the GIT quotient (P^1)^n//SL(2) with
respect to the symmetric linearization O(1,...,1). The intermediate blown-up
spaces turn out to be the moduli spaces of weighted pointed stable curves for
suitable ranges of weights. As an application, we provide a new unconditional
proof of M. Simpson's Theorem about the log canonical models of the
Mumford-Knudsen space. We also give a basis of the Picard group of the moduli
spaces of weighted pointed stable curves.Comment: An error (Lemma 5.3 in v1) has been corrected
GIT Compactifications of M_{0,n} and Flips
We use geometric invariant theory (GIT) to construct a large class of
compactifications of the moduli space M_{0,n}. These compactifications include
many previously known examples, as well as many new ones. As a consequence of
our GIT approach, we exhibit explicit flips and divisorial contractions between
these spaces.Comment: Final version to appear in Advance