Questions tagged [jacobians]
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9 questions from the last 365 days
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Jacobian of exponential map
I am playing around with the coarea formula and came across the problem of finding the Jacobian of the exponential map.
Let $G$ be a compact, semisimple Lie group with associated Lie algebra $\...
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Describing the compactified Jacobian of a nodal curve
$\DeclareMathOperator{\Pic}{Pic}$Let $C$ be an integral projective curve over $\mathbb C$, which is smooth except for a single node $x\in C$. Let $M$ be the moduli space of stable torsion-free sheaves ...
- 1,286
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Reference about the semiabelian variety associated to a stable curve
If a stable curve $C$ of genus $g$ is such that its dual graph has Betti number $1$, then the Jacobian of $C$ is a semiabelian variety of torus rank $1$. It is described by Mumford that the data of a ...
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What is the polarization type of the push-forward of the Poincaré-bundle to the Jacobian of a curve?
$\DeclareMathOperator{\Jac}{Jac}\DeclareMathOperator{\Pic}{Pic}$Let $C$ be a smooth curve of genus $g > 0$, and consider the Picard torus $\Pic^d(C)$ of line bundles of degree $d$. Let $\mathcal P$ ...
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Atkin-Lehner involution on the modular abelian varieties
Let $f$ be a CM modular forms with coefficients in the imaginary qudaratic field $K=Q(\sqrt{-3}))$ which correspond to an elliptic curve $E$ defined over $K$. Then Shimura constructed an abelian ...
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Numerical partial differentiation of a convolution product with FFT
How can one numerically calculate the partial derivatives of a convolution function, particularly when the closed-form or analytical expressions of the derivatives are not readily available? I am ...
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Numerical estimation of partial derivatives of convolved functions when closed forms do not exist
Summary: Some peak functions are convolutions which may not have a closed form solution. A classical example can that of a Voigt which is a convolution of a Lorentzian and a Gaussian, followed by ...
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Involution of the symmetric square of a smooth plane quartic
Let $C$ be a smooth plane quartic defined over a field $K$. Denote by $J$ its Jacobian, and by $C^{(2)}$ its symmetric square. Since $C$ is a smooth plane quartic, it is non-hyperelliptic, and hence ...
- 2,907
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Endomorphism ring of the Jacobian of a generic smooth plane quartic
Let $C$ be an arbitrary smooth plane quartic defined over a number field $K$. Assume $C$ is not hyperelliptic, and denote by $J$ the Jacobian of $C$. How does $\text{End}(J)$ look like for a generic ...
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