All Questions
9 questions
1
vote
1
answer
291
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Tangent space to spaces of maps
Let $B = \{x_1,\dots,x_{d-2},y_1,\dots,y_k\}$ be a subscheme of $d-2+k$ distinct points of $\mathbb{P}^1$, and $g:B\rightarrow \mathbb{P}^2$ be a morphism mapping $x_1,\dots,x_{d-2}$ to a fixed point $...
- 8,998
2
votes
0
answers
180
views
Linear projection from a point preserves flatness
Let $\pi:\mathcal{X} \to S$ be a flat family of affine curves contained in $\mathbb{C}^n$ for $n \ge 3$ i.e., $\mathcal{X} \hookrightarrow \mathbb{C}^n_S$ and the inclusion commutes with the natural ...
- 1,593
2
votes
1
answer
328
views
Where can I find a proof of identity of $H^1(X,T_X)$ and a quotient by the jacobian?
I'm reading some notes on hodge theory by Charles Siegel which makes a claim on page 16 relating the space of deformations of a smooth projective hypersurface $X$ with the jacobian ideal. More ...
- 1,716
7
votes
1
answer
769
views
Cohomology of tangent sheaf of a singular hypersurface
Let $X\subset\mathbb{P}^n$ be a hypersurface singular at finitely many points $p_i\in X$. We may assume that $X$ has ordinary singularities at the $p_i$'s.
Does there exists a formula, perhaps in ...
user91659
6
votes
2
answers
763
views
Automorphisms and infinitesimal deformations of a smooth complete intersection
Let $X\subset\mathbb{P}^{n+c}$ be a smooth complete intersection of dimension $n$.
Is it known when $Aut(X)$ is finite ?
Does there exist a formula for the dimension of the tangent space to the ...
user58018
2
votes
2
answers
575
views
Infinitesimal deformations of a fibration
Let $f:X\rightarrow Y$ be a morphism of normal projective varieties over an algebraically closed field with connected fibers.
Assume that both $Y$ and the general fiber of $f$ admit a non-trivial ...
user68440
4
votes
1
answer
433
views
Infinitesimal deformations of a singular projective surface
Let $X$ be a normal projective surface with just two singular points $x_1,x_2\in X$, where $X$ has rational quotient singularities.
Assume that both the singularities in $x_1$ and in $x_2$ admit a ...
user68440
19
votes
1
answer
2k
views
Accumulation of algebraic subvarieties: Near one subvariety there are many others (?), 3
Part 3 of this series of questions. In the meantime, I realized that there is some very simple question that was left open in Accumulation of algebraic subvarieties: Near one subvariety there are many ...
- 21.3k
27
votes
2
answers
3k
views
Accumulation of algebraic subvarieties: Near one subvariety there are many others (?)
Let's work over the field $\mathbb{C}$ of complex numbers, and let $X\subset \mathbb{P}^n$ be a projective variety. Let $\tilde{X}\subset \mathbb{P}^n$ be any small open neighborhood of $X$, in the ...
- 21.3k