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Full-Text Articles in Mathematics
Equivariant Smoothings Of Cusp Singularities, Angelica Simonetti
Equivariant Smoothings Of Cusp Singularities, Angelica Simonetti
Doctoral Dissertations
Let $p \in X$ be the germ of a cusp singularity and let $\iota$ be an antisymplectic involution, that is an involution free on $X\setminus \{p\}$ and such that there exists a nowhere vanishing holomorphic 2-form $\Omega$ on $X\setminus \{p\}$ for which $\iota^*(\Omega)=-\Omega$. We prove that a sufficient condiition for such a singularity equipped with an antisymplectic involution to be equivariantly smoothable is the existence of a Looijenga (or anticanonical) pair $(Y,D)$ that admits an involution free on $Y\setminus D$ and that reverses the orientation of $D$.
A Cone Conjecture For Log Calabi-Yau Surfaces, Jennifer Li
A Cone Conjecture For Log Calabi-Yau Surfaces, Jennifer Li
Doctoral Dissertations
In 1993, Morrison conjectured that the automorphism group of a Calabi-Yau 3-fold acts on its nef cone with a rational polyhedral fundamental domain. In this thesis, we prove a version of this conjecture for log Calabi-Yau surfaces. In particular, for a generic log Calabi-Yau surface with singular boundary, the monodromy group acts on the nef effective cone with a rational polyhedral fundamental domain. In addition, the automorphism group of the unique surface with a split mixed Hodge structure in each deformation type acts on the nef effective cone with a rational polyhedral fundamental domain. We also prove that, given a …
Boundary Divisors In The Moduli Space Of Stable Quintic Surfaces, Julie Rana
Boundary Divisors In The Moduli Space Of Stable Quintic Surfaces, Julie Rana
Doctoral Dissertations
I give a bound on which singularities may appear on KSBA stable surfaces for a wide range of topological invariants, and use this result to describe all stable numerical quintic surfaces, i.e. stable surfaces with K^2= 5, p_g=4, and q=0, whose unique non Du Val singularity is a Wahl singularity. Quintic surfaces are the simplest examples of surfaces of general type and the question of describing their moduli is a long-standing question in algebraic geometry. I then extend the deformation theory of Horikawa to the log setting in order to describe the boundary divisor of the moduli space of KSBA …