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

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

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

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

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

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

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### The isometry groups of flag manifolds

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

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

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

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

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### Relations between an projective variety and galois cohomology

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

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### G-modules and ideals of secant varieties

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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 $\mathbb{P}^n_K$?

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### A sub-variety of a Grassmannian

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### Semistable Higgs bundles and flat connections

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### Birational immersion of projective plane

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

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

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### Intersection multiplicity of limit linear spaces

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### homeomorphism type of punctured real projective spaces

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### Finite group action on quasi-projective varieties

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