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May
18
comment Extending the Abel-Jacobi map over the DM-compactification $\overline{\mathcal{M}}_2$?
I think Klaus Hulek and Sam Grushevsky had some results about this.
May
18
answered Torsion theory for quasi-coherent sheaves?
May
14
comment Matrix factorizations as a dg-category?
Have you looked into arxiv.org/abs/1308.0135?
May
8
comment Cohomology of conic bundle 3-folds
@FrancescoPolizzi: I think my argument works in positive characteristic as well.
May
8
comment Cohomology of conic bundle 3-folds
Another way to explain this is by noting that the derived pushforward of $O_X$ to the base $B$ of the conic bundle is $O_B$, so $H^3(X,O_X) = H^3(B,O_B) = 0$.
Apr
28
comment Is there an explicit way to glue a stable map in projective space by writing down the family of maps explicitly in terms of polynomials?
One of the ways is to find a map $P^1\times P^1 \to P^2$ such that on $P^1\times \{0\}$ it agrees with the first map and on $\{0\}\times P^1$ with the second. Then just restrict this map to the family of curves $x_1y_1 = tx_0y_0$ in $P^1\times P^1$.
Apr
23
answered Gluing locally free sheaves on curves
Apr
21
comment Morphism of modules of sections and pullback bundles
Use projection formula.
Apr
20
comment Why does this vector bundle on the surface sit in this exact sequence?
Correct. If $codim Z = 1$ then $I_Z$ is invertible and $N \otimes I_Z = N'$ with $N'$ a line bundle.
Apr
19
comment Why does this vector bundle on the surface sit in this exact sequence?
These are basic properties, try looking into Huybrechts--Lehn.
Apr
19
answered Why does this vector bundle on the surface sit in this exact sequence?
Apr
18
awarded  Nice Answer
Apr
16
comment Locally free sheaves and flat families of projective scheme
even with this --- take $X = Y = {\mathbb A}^1$. Then the only nonclosed point is the generic point and for it the tensor product is zero.
Apr
16
comment Locally free sheaves and flat families of projective scheme
No. Take $f$ to be identity and $F$ to be the structure sheaf of a point.
Apr
16
comment Does a fully faithful functor between triangulated categories induce embedding of their Grothendieck groups?
Density is a very strong assumption!
Apr
16
comment Deformation of curves and closed immersions
My impression was that the question asked whether the embedding of a special curve can factor through a LINEARLY embedded ${\mathbb P}^3$, and in this example it is embedded via the second Veronese embedding.
Apr
16
comment Vector bundle is semistable if only if it's pull back is semistable?
Simplest counterexample is $X = {\mathbb P}^2$, $D$ a line, $E = T_X$.
Apr
10
comment Are schemes which agree on open set and its complement equal? - w/ applications to initial ideals/tropical basis
An Artin subscheme of length 2 is a complete intersection of two hypersurfaces (say $x = y^2 = 0$), so I guess this still gives you a counterexample.
Apr
10
answered Are schemes which agree on open set and its complement equal? - w/ applications to initial ideals/tropical basis
Apr
4
comment What is the applications of the dg-enhancements of derived categories of sheaves
Whenever you want to perform some nontrivial construction with triangulated categories (e.g. gluing) you have to use enhancements.