If $S$ is a graded ring which is generated by $S_1$ as an $S_0$-algebra and $X=\operatorname{Proj}S$, do we have $\mathcal O_X(1)(X)=S_1$?
2026-03-25 06:19:25.1774419565
Do we have $\mathcal O_X(1)(X)=S_1$?
102 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ALGEBRAIC-GEOMETRY
- How to see line bundle on $\mathbb P^1$ intuitively?
- Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.
- Is $ X \to \mathrm{CH}^i (X) $ covariant or contravariant?
- An irreducible $k$-scheme of finite type is "geometrically equidimensional".
- Global section of line bundle of degree 0
- Is there a variant of the implicit function theorem covering a branch of a curve around a singular point?
- Singular points of a curve
- Find Canonical equation of a Hyperbola
- Picard group of a fibration
- Finding a quartic with some prescribed multiplicities
Related Questions in SHEAF-THEORY
- Is $ X \to \mathrm{CH}^i (X) $ covariant or contravariant?
- Question about notation for Čech cohomology and direct image of sheaves in Hartshorne
- Does sheafification preserve surjectivity?
- Image of a morphism of chain complexes of sheaves via direct/inverse image functor
- Tensor of a $k[X]$ module with the structure sheaf of an affine variety is a sheaf
- Sheafy definition for the tangent space at a point on a manifold?
- Whats the relationship between a presheaf and its sheafification?
- First isomorphism theorem of sheaves -- do you need to sheafify if the map is surjective on basis sets?
- An irreducible topological space $X$ admits a constant sheaf iff it is indiscrete.
- Why does a globally generated invertible sheaf admit a global section not vanishing on any irreducible component?
Related Questions in GRADED-RINGS
- Extending a linear action to monomials of higher degree
- Direct sum and the inclusion property
- High-degree pieces of graded ideal with coprime generators
- Bihomogeneous Nullstellensatz
- The super group $GL(1|1)$
- Properties of the Zariski topology on Proj
- Localization of a graded ring at degree zero
- Adams operations and an artificial grading on K-theory
- On "homogeneous" height and "homogeneous" Krull-dimension?
- Units are homogeneous in $\mathbb Z$-graded domains
Related Questions in GRADED-MODULES
- On "homogeneous" height and "homogeneous" Krull-dimension?
- Units are homogeneous in $\mathbb Z$-graded domains
- In a $\mathbb Z$-graded ring we have $IR \cap R_0 = I$
- Are the associate primes of a graded module homogeneous?
- Meaning of "graded $R$-modules" in May's "A Concise Course in Algebraic Topology" on Page 89
- The Endomorphism algebra of graded vector space
- Modules can be viewed as monoid objects in some appropriate monoidal category?
- Proving that $\operatorname{Tor}_n^R$ is a bifunctor
- Singular chain complex as a graded algebra
- Tensor product of graded algebras 3
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- 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?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- 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
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
If $S$ is a polynomial ring this is Hartshorne Prop II.5.13.
If $S$ is not a polynomial ring then this is not generally true. Exercise 5.14 provides a counterexample.