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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

3 votes
1 answer
188 views

Image, upto direct summands, of derived push-forward of resolution of singularities

Let $\mathcal C$ be a full subcategory (closed under isomorphism also) of an additive category $\mathcal A$. Then, $\text{add}(\mathcal C)$ is the full subcategory of $\mathcal A$ consisting of all ob …
6 votes
1 answer
322 views

When can we choose non-zero-divisor $x\in \mathfrak m$ in a reduced local ring $(R,\mathfrak...

Let $(R,\mathfrak m)$ be a local Cohen-Macaulay reduced ring of dimension at least $2$. Then, can we find a non-zero-divisor $x\in \mathfrak m$ such that $R/xR$ is again a reduced ring? If needed, I a …