I am having trouble understanding the concept of smooth completions of algebraic curves. I know the definition (smooth, complete curves which contain the curve X as an open subset ) and according to Wikipedia they are even unique over perfect fields. But how can I construct a smooth completion of a given curve? Are they the same as projective closures?
2025-01-13 09:35:05.1736760905
Smooth completion of algebraic curves
541 Views Asked by Belmont https://math.techqa.club/user/belmont/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 ALGEBRAIC-CURVES
- Generic point and pull back
- Every point lies on a unique secant through $C$
- There exists a divisor linearly equivalent to $P$ not containing $P$
- bases of a function field
- Dimension of homogeneous polynomials passing through 4 points
- Can a polynomial of degree 2 vanish on three different lines?
- If for any external point, exactly two tangents can be drawn to an algebraic curve, must the curve be a conic?
- Linking regularity of ideal sheaf with Fitting ideals sheaf
- Degree of pull-back of locally free sheaves under normalization
- Any higher level maths or theories for epicycloids and/or hypocycloids?
Related Questions in PROJECTIVE-GEOMETRY
- Projective transformation in $\mathbb{P}^1$
- An irreducible quadric hypersurface is rational?
- Transforming a curve to pass through given points
- How to prove this hypothesis on convex geometry viewed orthogonally down cartesian axes?
- Plucker's $\mu$
- Can a polynomial of degree 2 vanish on three different lines?
- Relation between curves on a surface and divisors
- How do I construct a 4 sided 45 degree pyramid from four triangular planes ( open on bottom )
- What is the point of having at least three points on every line of a projective plane?
- Does the circle in the Fano plane have to be closed?
Related Questions in FORMAL-COMPLETIONS
- Motivation of completions of schemes?
- Direct limit of completions of finitely generated submodules
- Smooth completion of algebraic curves
- completion and heights of prime ideals
- Commutative Algebra "mess": recover the complete local rings of the normalization
- Extension of DVRs and uniformizers
- How can I compute completions of rings?
- $p$-adic completion of $\mathbb Z((t))$
- Completion given a partial order
- If $M$ is a $R$-module in a $K$-vector space $V$, is $\widehat M \cap V = M_{\mathfrak p}$?
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