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May 18 |
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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 |
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Matrix factorizations as a dg-category?
Have you looked into arxiv.org/abs/1308.0135? |
May 8 |
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Cohomology of conic bundle 3-folds
@FrancescoPolizzi: I think my argument works in positive characteristic as well. |
May 8 |
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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 |
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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 |
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Morphism of modules of sections and pullback bundles
Use projection formula. |
Apr 20 |
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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 |
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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 |
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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 |
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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 |
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Does a fully faithful functor between triangulated categories induce embedding of their Grothendieck groups?
Density is a very strong assumption! |
Apr 16 |
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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 |
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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 |
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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. |