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EDIT: If the question is for SE level just delete from here as it is also posted there. In fact I have seen some questions in SE regarding the coordinate rings of product of projective varieties but n …

I need some help in order to clarify some topological data of a $K3\times T^{2}$ Calabi Yau manifold in which $K3$ part has been obtained as a resolution of a $T^{4}/ \mathbb{Z_{2}}$ orbifold . ED …

Could anyone cite some applications or developments in mathematical physics or string theory that use schemes? I find curious the fact that while things like derived algebraic geometry and stacks hav …

Let $Vect_{n}(C)$ the moduli stack of vector bundles $V$ of rank $n$ over a smooth curve $C$ of genus $g$. It is well known that $Vect_{n}(C)$ is a smooth stack of dimension $\dim(H^{0}(C,End(V)))-\ …

I am interested in the concept of dimension of derived and $n$-Artin stacks. Take for example the definition 4.10 of From HAG to DAG: derived moduli stacks. in which they define the dimension of a ta …

As the visuallization of an algebraic stack is virtually impossible I warn about this is a soft question. I am interested in thinking visually about algebraic stacks (also higher and derived stacks, …

I am trying to develop a geometrical intuition for "higher spaces", i.e. both in the sense of higher dimensional spaces (more than three dimensions) and in the sense of abstractions beyond manifolds a …

I am a beginner in derived algebraic geometry and I am trying to develop some visual and geometrical intuition about derived schemes (and stacks), or more precisely about the new geometrical phenomena …

One of the most famous examples of higher Artin stacks is the stack of perfect complexes. I recall here the basic stuff: We fix a function $b: \mathbb{Z} \rightarrow \mathbb{N}$ which is zero outsid …

I am thinking about higher Artin stacks in the sense of Simpson, concretely I would like to calculate the dimension and compare these two cases: $\mathfrak{X}_{1}=$ Higher linear stack classifying ( …