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Results tagged with ag.algebraic-geometry
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user 173545
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
2
votes
Accepted
Most general lifting property for proper morphisms
I don't have a description of the class of morphisms you are describing, but let me provide a counterexample in your case of interest that can perhaps limit your search for a general result. Consider …
4
votes
0
answers
310
views
Edge morphisms on the Grothendieck spectral sequence in the case that one of the functors is...
Let $\mathcal{A}, \mathcal{B}, \mathcal{C}$ be abelian categories and let $G: \mathcal{A} \to \mathcal{B}, F: \mathcal{B} \to \mathcal{C}$ be left exact functors, with the hypotheses needed to apply t …
5
votes
0
answers
694
views
Spectral sequence from a stratification by closed subvarieties
I am looking for a reference for the following result: If $X$ is an algebraic variety and
$$X = T_n \supset T_{n-1} \supset \cdots \supset T_{-1} = \varnothing$$
is a stratification (edit: filtration) …
3
votes
1
answer
282
views
Equivalent definitions of normality for complex algebraic varieties
In Kollár's article The structure of algebraic threefolds: an introduction to Mori's program he gives the following definition of a normal variety:
Definition 5.4. Let $V \subset \mathbb{C}^n$ be an …
2
votes
1
answer
156
views
Pullback morphism of a hyperplane inclusion is zero in the derived category
Let $L \subset \mathbb{C}^n$ be a hyperplane and let $i:L \to \mathbb{C}^n$ be the inclusion. Since $i$ is proper, we have induced maps $i^*: H^k_c(\mathbb{C}^n) \to H^k_c(L)$, and these maps are zero …