# Tagged Questions

Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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### Non-algebraic Hecke characters

Algebraic Hecke characters are ubiquitous in modern number theory. They are in 1-1 correspondence with one dimensional complex Galois representations, and in some precise sense they are the building ...
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### irreducibility of discriminant

This must be well-known to everyone but me, but here goes: take a general (monic) polynomial $p(x) = x^d + a_{d-1} x^{d-1} + \dotsc + a_0.$ The discriminant is a polynomial $D(a_0, \dotsc, a_{d-1}).$ ...
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### Vector field on a K3 surface with 24 zeroes

In http://mathoverflow.net/a/44885/4177, Tilman points out that one can use a $K3$ surface minus the zeroes of a generic vector field to build a nullcobordism for $24[SU(2)]$. Given that a) this is a ...
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### Normalization of a Noetherian local domain and line bundles on the punctured spectrum

Let $A$ be a Noetherian local domain ($2$-dimensional if needed) such that its punctured spectrum $U$ is regular, and let $A'$ be the normalization of $A$. 1) Is it possible for $A'$ to have ...
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### Universal property of limits of invertible sheaves

Let $R$ be a discrete valuation ring, $m$ the maximal ideal and $f:X \to \mathrm{Spec}(R)$ be a flat, proper morphism of relative dimension $1$. Assume further that $X$ is regular. For any $n>0$, ...
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### Are holomorphic quasi-positive line bundles on a Kähler manifold positive?

Holomorphic quasi-positive line bundles on a complex manifold $M$ are line bundles whose chern class can be represented by a closed $(1,1)$-form which is quasi-positive, that is, non-negative at all ...
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### change of the residue of meromorphic differential by a covering map.

Let $C_1$ and $C_2$ denote complex algebraic curves, and let $f : C_1 \rightarrow C_2$ be a non-constant map. Let $x$ be a point on $C_1$ and its ramification degree is $e_x$. I want to compute the ...
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### Singularities of complete intersections of affine varieties with hypersurfaces

Let $k$ be a field of characteristic $0$ (not necessarily algebraically closed), and let $A=k[x^1,\ldots,x^m]/(f_1,\ldots,f_N)$ be an affine variety which is a complete intersection; i.e. ...