Does someone have a quick and direct argument that infinitesimal deformations of an affine smooth variety over a field $k$ are only the trivial infinitesimal deformations? (without previous construction of the functors $T^i$ of the cotangent complex)
2025-01-13 02:13:10.1736734390
Affine smooth variety has only trivial first-order deformations
580 Views Asked by Angelo https://math.techqa.club/user/angelo/detail AtRelated Questions in ALGEBRAIC-GEOMETRY
- Relations among these polynomials
- Completion of a flat morphism
- Is every sheaf a subsheaf of a flasque sheaf?
- Intersection of curves on surfaces and the sheaf $\mathcal O_{C\cap C'}$
- Does intersection of smooth divisors satisfy Serre $S_2$ criterion?
- Application of GRR in number theory
- Generic point and pull back
- Every point lies on a unique secant through $C$
- Projective transformation in $\mathbb{P}^1$
- Equality $H^i(K,\mathcal{F}_{|K})=\varinjlim_{U\supset K}H^i(U,\mathcal{F}_{|U})$ for a constructible sheaf
Related Questions in HOMOLOGICAL-ALGEBRA
- Are there right-deformations for abelian sheaves?
- Obstruction to be conjugated by an automorphism for subgroups of an abelian group
- Galois cohomologies of an elliptic curve
- Generalization for Leray Hirsch theorem for Principal $G$-bundle
- Projective resolutions of modules in a short exact sequence (Dummit & Foote Proposition 17.1.7)
- Can we produce a long exact sequence in cohomology from more than just short exact sequences?
- Affine smooth variety has only trivial first-order deformations
- What is an additive functor?
- Compute $\text{Tor}^R_n(M,M)$ in the following specific case.
- Group (co)homology with coefficients in a tensor product
Related Questions in DEFORMATION-THEORY
- Behaviour of Chern class under deformation
- Affine smooth variety has only trivial first-order deformations
- Deformation theory introduction without unnecessary machinery
- Normal Space of an orbit at a point
- Exercise from "Moduli of Curves"
- How is the smoothness of the space of deformations related to unobstructedness?
- Serre duality explicitly on curves
- Flat schemes over artinian local ring with isomorphic special fibers
- $T^i$ functors in Hartshorne's Deformation Theory
- Normal bundle to doubled line on cubic surface
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity