We let $S$ be a graded algebra. I have a 2 questions regarding the Proj construction.
- It seems to me that we do not know what $O_{Proj S}Proj(S))$ is ?
- How is the map $S_0 \rightarrow \Gamma(Proj S, O_{Proj(S)})$ induced?
2026-03-25 02:56:33.1774407393
Projective space $Proj$
273 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated 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 AFFINE-SCHEMES
- Can find common principal open subsets in the intersection of two open affine subschemes
- Give an example of a scheme $X$ so that the asbolute Frobenius morphism induces an isomorphism on global sections.
- $K(Y)$ is isomorphic to the quotient field of $A(Y).$
- References for sufficiency of tangential criteria for formally smooth/unramified/étale morphisms
- Geometric viewpoint on $\Bbbk[t]\to \Bbbk(t)$ not being of finite type
- Affine Schemes and Basic Open Sets
- compute $ \operatorname{Spec}\mathbb{Z}[x,y]/(x^2+y^2-n) $
- Meaning of $f$ being a function on $\text{Spec}(A)$
- (Connected) non-contractible schemes
- Dimension of the tangent cone of $V(\mathfrak{a})$
Related Questions in PROJECTIVE-SCHEMES
- Do torsion-free $\mathcal{O}_X$-modules on curves have dimension one?
- Proper curves over some field are projective
- Global section $s$ of ample line bundle such that $X_s$ is everywhere dense
- Finite morphism $f:X \to \mathbb{P}_k^n$ is surjective?
- Conditions on $\mathcal{F}$ such that $\chi(\mathcal{F}) = 0$ for a coherent sheaf on a curve over $k$.
- Calculating Euler Characteristic of Closed Subscheme
- How to choose coordinates for a projective scheme.
- Properties of the Zariski topology on Proj
- The vanishing scheme of for a graded ring generated by elements of degree 1 (Vakil 4.5.P)
- Global sections of projective schemes
Related Questions in QUASICOHERENT-SHEAVES
- Why is every sheaf of $\mathcal{O}_{X}$-modules not generated by global sections?
- Free module after tensoring with a flat local ring
- On the support of sheaf of modules or quasi-coherent sheaves over ringed spaces
- QCQS lemma for modules?
- Gaga and quasicoherent sheaf
- Counter-examples for quasi-coherent, coherent, locally free and invertible sheaves
- $f_* f^* \mathcal{G}= \mathcal{G}$ and $f^* f_* \mathcal{F}= \mathcal{F}$ for Quasicoherent Sheaves
- Why are the noetherian objects in a category of quasicoherent sheaves just the coherent ones?
- Is this exact: $0\to\mathcal{O}^{hol}\to\mathcal{O}(p)\to \Bbb{C}_p,$
- Quasicoherent sheaves on the groupoid of vector bundles on a surface
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?