# 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

**1**

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

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### Projective embeddings of quotients of normal varieties

**2**

**1**answer

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

**2**

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

**2**

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### Bertini theorem for connectedness

**3**

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

**1**

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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?

**3**

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

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### Is projective closure of a regular affine algebraic set also regular?

**2**

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### What is the precise relationship between projective duality and the Radon transform?

**7**

**1**answer

### Combinatorial curves in combinatorial projective planes

**2**

**1**answer

### Morphisms from projective space to lower dimension spaces [duplicate]

**2**

**1**answer

### Representability of Grassmannian functor by a scheme

**0**

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### The Grothendieck ring of varieties with classical Zariski

**1**

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### Cohomological criterion for being projectively normal

**3**

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### Existence of regular hypersurface sections

**2**

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### Intersection of two quadrics in $\mathbb{R} P^5$

**12**

**1**answer

### An inverse problem for Grothendieck rings of varieties

**1**

**1**answer

### Image of smooth curve containing the image of a point as smooth point

**2**

**0**answers

### Graded Betti numbers $\beta_{n,j}$ for points in $\mathbb{P}^n$

**2**

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### Embedding of $CP^2/CP^1$ into euclidean space [closed]

**3**

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### Coordinate ring of complete intersection Calabi Yau (CICY)

**6**

**1**answer

### Moduli space of flat connections over a Riemann surface

**2**

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### Moduli space is a Calabi-Yau manifold?

**2**

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### The isometry groups of flag manifolds

**4**

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### Complex projective algebraic variety, moduli space of flat connections, and instantons

**3**

**1**answer

### A non-rational variety with a full exceptional collection?

**8**

**1**answer

### The different gradings of a graded ring, and their schemes

**0**

**1**answer

### Fiber product of projective varieties and ample line bundles

**4**

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### Relations between an projective variety and galois cohomology

**7**

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### What can be said about the topological K-theory of non-singular varieties of small codimension in projective space?

**10**

**1**answer

### G-modules and ideals of secant varieties

**3**

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### Given an embedding of $X$ into $\mathbb{P}^n_K$, do you get an induced embedding of any twist of it into $\mathbb{P}^n_K$?

**4**

**1**answer

### A sub-variety of a Grassmannian

**2**

**1**answer

### Semistable Higgs bundles and flat connections

**0**

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### Birational immersion of projective plane

**2**

**1**answer

### Where can I find a proof of identity of $H^1(X,T_X)$ and a quotient by the jacobian?

**2**

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### What techniques are available for constructing D-modules over smooth projective varieties?

**4**

**1**answer

### Intersection multiplicity of limit linear spaces

**2**

**1**answer

### homeomorphism type of punctured real projective spaces

**4**

**1**answer

### Finite group action on quasi-projective varieties

**1**

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