Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTowards a Classification of Rigid Product Quotient Varieties of Kodaira Dimension 0
144
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper the authors study quotients of the product of elliptic curves by a rigid diagonal action of a finite group $G$. It is shown that only for $G = operatorname{He(3)}, mathbb Z_3^2$, and only for dimension $geq 4$ such an action can be free. A complete classification of the singular quotients in dimension 3 and the smooth quotients in dimension $4$ is given. For the other finite groups a strong structure theorem for rigid quotients is proven.
rate research
Read More
For each $n geq 3$ the authors provide an $n$-dimensional rigid compact complex manifold of Kodaira dimension $1$. First they construct a series of singular quotients of products of $(n-1)$ Fermat curves with the Klein quartic, which are rigid. Then using toric geometry a suitable resolution of singularities is constructed and the deformation theories of the singular model and of the resolutions are compared, showing the rigidity of the resolutions.
In this paper we will prove a uniformity result for the Iitaka fibration $f:X rightarrow Y$, provided that the generic fiber has a good minimal model and the variation of $f$ is zero or that $kappa(X)=rm{dim}(X)-1$.
Using Galois theory, we construct explicitly (in all complex dimensions >1) an infinite family of simple complex tori of algebraic dimension 0 with Picard number 0.
Over the past two decades, there has been much progress on the classification of symplectic linear quotient singularities V/G admitting a symplectic (equivalently, crepant) resolution of singularities. The classification is almost complete but there is an infinite series of groups in dimension 4 - the symplectically primitive but complex imprimitive groups - and 10 exceptional groups up to dimension 10, for which it is still open. In this paper, we treat the remaining infinite series and prove that for all but possibly 39 cases there is no symplectic resolution. We thereby reduce the classification problem to finitely many open cases. We furthermore prove non-existence of a symplectic resolution for one exceptional group, leaving 39+9=48 open cases in total. We do not expect any of the remaining cases to admit a symplectic resolution.
In this note, we apply the semi-ampleness criterion in Lemma 3.1 to prove many classical results in the study of abundance conjecture. As a corollary, we prove abundance for large Kodaira dimension depending only on [BCHM10].
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
