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Cranium Clamp
  • Member for 4 years, 10 months
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Closed embedding into weighted projective stack/space
Am I misunderstanding something? The coarse moduli space is just ordinary $ \mathbb{P}^n $ in that case, no?
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Closed embedding into weighted projective stack/space
@JasonStarr i agree, but that was for weights equal to 1. And when all weights are equal, the second question has that answer an easy answer. In general, I was just looking whether there are conditions on sections of tensor powers of a line bundle to give a closed embedding.
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Exercise 1.5.8 from Robin Hartshorne's Deformation Theory
Yes, that’s true. Since I was just looking for a general reference for your question, I put in that link.
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Exercise 1.5.8 from Robin Hartshorne's Deformation Theory
Any morphism from a variety $ X $ to $ Hilb $ can be understood by understanding it on its geometric points. This is in Hartshorne (his original book) as the t-functor in chapter 2.
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K3 surfaces with no −2 curves
@YCor yes, take any K3 surface. The second cohomology with the intersection product is isomorphic as a lattice to E8^2 + U(-2)^3 for any K3 surface.
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Fourier-Mukai transform is the derived functor
Not to be rude but if you cannot see it, why have doubts on it? This is literally flat base change at work.
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Understanding the universal family $\mathcal{M}_{g,1}\to\mathcal{M}_g$
math.stackexchange.com/questions/4482388/… I wrote down an answer at MSE for the same thing. It's been a while but maybe it helps.
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What is the restriction of the tangent bundle on a projective space to a rational curve
@user145752 the normal bundle of a line in P^n is n-1 copies of O(1). Now $ i^* \mathbb{P}^n $ sits in between O(2) and the normal bundle, so has to be the direct sum because of vanishing Ext..