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We classify all $n$-dimensional reduced Cohen-Macaulay modular quotient variety $mathbb{A}_mathbb{F}^n/C_{2p}$ and study their singularities, where $p$ is a prime number and $C_{2p}$ denotes the cyclic group of order $2p$. In particular, we present an example that demonstrates that the problem proposed by Yasuda cite[Problem 6.6]{Yas2015} has a negative answer if the condition that $G$ is a small subgroup was dropped.
Let $Gsubseteq GL(n)$ be a finite group without pseudo-reflections. We present an algorithm to compute and verify a candidate for the Cox ring of a resolution $Xrightarrow mathbb{C}^n/G$, which is based just on the geometry of the singularity $mathbb
We give a version in characteristic $p>0$ of Mumfords theorem characterizing a smooth complex germ of surface $(X,x)$ by the triviality of the topological fundamental group of $U=Xsetminus {x}$. This note relies on discussions the authors had durin
We describe the birational and the biregular theory of cyclic and Abelian coverings between real varieties.
In this paper we generalize the definitions of singularities of pairs and multiplier ideal sheaves to pairs on arbitrary normal varieties, without any assumption on the variety being Q-Gorenstein or the pair being log Q-Gorenstein. The main features
We construct a global B-model for weighted homogeneous polynomials based on K. Saitos theory of primitive forms. Our main motivation is to give a rigorous statement of the so called global mirror symmetry conjecture relating Gromov-Witten invariants