论文标题
美元
$\mathbb{Z}/2\mathbb{Z}$-Equivariant smoothings of cusp singularities
论文作者
论文摘要
让$ p \ in x $成为尖尖的奇异性的细菌，让$ r $是一种反拼双面的交流，这是一种互动，因此在$ x \ setMinus \ {p \}上无处可消失的全面塑料2形$ω$，用于哪些$^*（对于哪个$^*（$^*（p \}））。还假设，在$ x \ setminus \ {p \} $上免费固定点免费。我们证明，对于这种具有反共计性交流的这种奇异性的足够条件是具有等效性的，这是存在looijenga（或反典型）对（y，d）$的存在，该$（y，d）承认对$ y \ y \ y \ y \ setminus d $免费无关，而这反向$ d $ $ d $。这项工作还包含了$ \ mathbb {z}/2 \ mathbb {z} $ - 简单椭圆形奇异性$ p \ in C（e）$带有$ e $ e $ e $ e椭圆曲线$ d \ leq 8 $的简单椭圆形的$ p \ e \ e $ d \ leq d \ leq 8 $的简单平稳性的证明证明了$ \ mathbb {z}/2 \ mathbb {z}/2 \ mathbb {z} $ - equivariant的平稳性$ \ mathbb {z}/2 \ mathbb {z} $ - action。
Let $p\in X$ be the germ of a cusp singularity and let $ι$ be an antisymplectic involution, that is an involution such that there exists a nowhere vanishing holomorphic 2-form $Ω$ on $X\setminus \{p\}$ for which $ι^*(Ω)=-Ω$. Assume also that the involution is fixed point free on $X\setminus\{p\}$. We prove that a sufficient condition 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 $D$. This work also contains the proof of an analogue necessary and sufficient condition for the $\mathbb{Z}/2\mathbb{Z}$-equivariant smoothability of simple elliptic singularities $p\in C(E)$ with $E$ an elliptic curve of degree $d\leq 8$ and even equipped with a $\mathbb{Z}/2\mathbb{Z}$-action.
