# Questions tagged [projective-varieties]

In algebraic geometry, a projective variety over an algebraically closed field $k$ is a subset of some projective $n$-space $\mathbb P^n$ over $k$ that is the zero-locus of some finite family of homogeneous polynomials of $n + 1$ variables with coefficients in $k$, that generate a prime ideal, the defining ideal of the variety

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### dimension of linear system and multiplicity at a point

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### showing a plane curve non-generic by exhibiting an even divisor

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### Nodes of rational plane sextic curves

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### Description of determinantal varieties in $\mathbb{P}^n$ that are linear sections of determinantal varieties in $\mathbb{P}^{n+1}$

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### Irreducibility of the base and of the general fiber

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### Determinantal representation of joins

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### Consequence of the failure of Nagata's conjecture

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### What is the étale fundamental group of projective spaces over finite fields?

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### Pencil of divisors in algebraic geometry

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### Degree of a variety vs degree of its blow-up

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### Generalization of universal sequence over Grassmannians

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### Functorial lift of certain vector bundles to the ambient projective space

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### Injectivity of pushforward of rational Chow groups

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### Linear spaces secant to Veronese varieties

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### How to write down an explicit equation of given degree yielding a smooth hypersurface in a projective space?

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### Chow's Lemma: Mumford's and Grothendieck's (?) definitions

**4**

**3**answers

### Irreducible components: associativity for intersections?

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### Sections of vector bundles interpreted as sections of line bundles

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**1**answer

### existence of birational morphism and divisors

**3**

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### How many holes may a projection of an algebraic variety have?

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### Comparison of classical and Zariski topologies with constructible sets

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### Does the Jacobian ring of a weighted projective hypersurface determine it up to isomorphism?

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### Unibranch points (definition for varieties over arbitrary field)

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### Mathematical pendulum and $\mathbb C P^n$

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### Blow-up of projective variety $P^1 \times P^1… \times P^1$ ($n$ times) and blow-up of $P^n$

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### Strict transform of a tangent curve under blow-up

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### Projective space over general schemes as quotient

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### Berkovich Integration on algebraic curves

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**1**answer

### Question about Correspondences from Mumford’s Complex Projective Varieties

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### High direct image of dualizing sheaf

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### Reference for the multiprojective Nullstellensatz?

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### Corollary of Mori’s theorem

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### Finite maps to normal varieties have fibers with bounded number of points

**14**

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### Recover the characteristic of $k$ from the category of $k$-varieties

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### Kan liftings and projective varieties

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### Degree of secant varieties of Veronese varieties

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### Clemens-Griffiths component birational invariant

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### On relating $l(A), l(B)$ and $l(A+B)$ for Weil divisors on a smooth projective curve where one of the divisors is effective

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### Embedding Calabi-Yau manifolds in projective space

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### About the multiplicity of intersection in projective space

**1**

**1**answer

### Non-unique completion of a flat family of smooth projective varieties

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### Projective embeddings of quotients of normal varieties

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### Closed points of a closed subscheme of $\mathbb{P}^n$ over the residue field and the fraction field of a valuation ring $R$

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### Chow form of closure of product of affine varieties given the chow forms of their closurs

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### Bertini theorem for connectedness

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### When is the pushout of projective varieties along embeddings a projective variety?

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### Ample line bundle gives alternative description of a variety

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### Why can we require that the hyperdeterminant has integral coefficients?

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### When is a monomial rational map on the projective space birational?

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**1**answer