论文标题
极端1/2 Calabi-yau 3倍和六维F理论应用
Extremal 1/2 Calabi-Yau 3-folds and six-dimensional F-theory applications
论文作者
论文摘要
我们讨论了一种分类1/2 calabi-yau 3倍的奇异性类型的方法，这是一个在先前的研究中引入的有理椭圆形的3倍家庭，涉及6D F理论模型中的各种U（1）因子。 Mukai最近研究的一对射双Del Pezzo歧管用于分析奇异性类型。特别是，我们研究了最大排名的七种奇异性类型的1/2 calabi-yau 3倍。使用爆炸分析奇异纤维的结构。还讨论了Calabi-yau 3倍的六维$ n = 1 $ f理论的1/2 calabi-yau 3倍3倍椭圆形的椭圆形的Calabi-yau和应用3倍。推导的奇异纤维在研究以6D理论压缩形成的量规组中应用。用于分析本研究中使用的奇异纤维和截面的爆破方法可能在研究6D F理论中U（1）中收取的U（1）因子和超多种方面有应用。
We discuss a method for classifying the singularity types of 1/2 Calabi-Yau 3-folds, a family of rational elliptic 3-folds introduced in a previous study in relation to various U(1) factors in 6D F-theory models. A projective dual pair of del Pezzo manifolds recently studied by Mukai is used to analyze the singularity types. In particular, we studied the maximal rank seven singularity types of 1/2 Calabi-Yau 3-folds. The structures of the singular fibers are analyzed using blow-ups. Double covers of the 1/2 Calabi-Yau 3-folds yield elliptic Calabi-Yau 3-folds and applications to six-dimensional $N = 1$ F-theory on the Calabi-Yau 3-folds are also discussed. The deduced singular fibers have applications in studying the gauge groups formed in 6D F-theory compactifications. The blow-up methods used to analyze the singular fibers and sections utilized in this research might have applications in studying the U(1) factors and hypermultiplets charged under U(1) in 6D F-theory.
