# Questions tagged [picard-scheme]

In algebraic geometry, the scheme that represents the Picard functor and the natural generalisation of the Picard variety for a given algebraic variety to the theory of schemes. If your question is not about algebraic or arithmetic geometry, then this is likely not the right tag to use.

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### Irreducibility of the Jacobians of a curves.

I'm studying Jacobian varieties.I assume that the existence of the Jacobian variety for a curve and attempt to show irreducibility of the Jacobian for a curve according to Remark:IV.4.10.9 of ...
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### Picard's method does not solve first order differential equation?

I have the following first order differential equation $$x^\prime(t)=-(x(t))^2+2x(t),\quad t\geq 0,\quad x(0)=1$$ Now I want to obtain an approximation of $x(t)$ by using Picard's method. Then the ...
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### Definition of $\operatorname{Pic}^0(V)$ for $V$ a singular variety

How does one define the $\operatorname{Pic}^0(V)$ for $V$ being a singular, not necessarily normal variety? Until now the approach I found by searching Google is to prove that the Picard functor is ...
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### Is the Picard group computable by a computer algebra system?

My question is, as the title suggests: Given the defining ideal of a variety $X$ (over $\mathbb C$), can we compute $Pic(X)$ with a computer algebra system? Even if the answer is no in general, are ...
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### Group law for an elliptic curve using schemes

I was trying to understand better the definition of the group law for an elliptic curve given in Katz and Mazur's book (http://books.google.com.br/books/about/Arithmetic_Moduli_of_Elliptic_Curves.html?...