New posts in algebraic-geometry

divisor class group of a product of schemes

algebraic-geometry schemes

Reality check: $\mathcal{O}_{\mathbb{P}_\mathbb{R}^1}(1)$ and $\mathcal{O}_{\mathbb{P}_\mathbb{R}^1}(-1)$ are both Möbius strips?

algebraic-geometry differential-topology schemes vector-bundles coherent-sheaves

Show that there exists a regular function that is not a quotient of polynomials

algebraic-geometry affine-geometry

If $A$ is a finitely generated $k$-algebra with no nontrivial maps $m/m^2\to k$ for any $m\subset A$, is $A\cong k^n$ as modules?

abstract-algebra algebraic-geometry commutative-algebra

Is a scheme with a single closed point affine?

algebraic-geometry

Closed subscheme of a projective scheme determined by homogeneous ideals

algebraic-geometry schemes

Suppose $G$ and $G'$ are grobner bases for the ideal $I$. Show that $\overline{f}^{G} = \overline{f}^{G'}$ for $f \in k[x_1, \cdots, x_n]$

algebraic-geometry groebner-basis

Equivalent definitions of Noetherian topological space

general-topology algebraic-geometry commutative-algebra

How to tell whether a scheme is reduced from its functor of points?

algebraic-geometry schemes

Hartshorne II Exercise 8.2

algebraic-geometry

In which cases does pullback commute with the Hom-sheaf?

algebraic-geometry category-theory sheaf-theory

Irreducible fibers of a closed subset implies irreducibility

algebraic-geometry

Elliptic curve over algebraically closed field of characteristic $0$ has a non-torsion point

number-theory algebraic-geometry field-theory elliptic-curves abelian-varieties

Trying to understand open (closed) subfunctors

algebraic-geometry

Rings whose spectrum is Hausdorff

algebraic-geometry commutative-algebra

Is there a General Formula for the Transition Matrix from Products of Elementary Symmetric Polynomials to Monomial Symmetric Functions?

combinatorics algebraic-geometry polynomials symmetric-functions

The coarse moduli space of a Deligne-Mumford stack

algebraic-geometry moduli-space

Topology of "degenerate spectrum submanifold" in the space of hermitian matrices

linear-algebra differential-geometry algebraic-geometry algebraic-topology algebraic-groups

Regular local ring and a prime ideal generated by a regular sequence up to radical

algebraic-geometry commutative-algebra

Intuition behind isomorphism of algebraic varieties

algebraic-geometry intuition