Defining supermanifolds by equations
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I would like to in what sense supermanifolds may be defined by systems of equations in the ordinary flat superspace. I am particularly interested in the approach to supergeometry via ringed spaces.
Remark: situation is quite clear for me in the case of affine super schemes. In this case subscheme of the spectrum $mathrm{Spec}(mathcal A)$ of the supercommutative superalgebra $mathcal A$ which may be described as the zero locus of an ideal $J subseteq mathcal A$ is simply the spectrum of the supercommutative superalgebra $frac{mathcal A}{J}$. We have a canonical morphism $mathrm{Spec} left (frac{mathcal A}{J} right ) to mathrm{Spec}(mathcal A)$. This construction doesn't seem to easily generalize to supermanifolds.
differential-geometry algebraic-geometry superalgebra supermanifolds supergeometry
asked Nov 17 at 10:52
Blazej
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up vote
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I would like to in what sense supermanifolds may be defined by systems of equations in the ordinary flat superspace. I am particularly interested in the approach to supergeometry via ringed spaces.
Remark: situation is quite clear for me in the case of affine super schemes. In this case subscheme of the spectrum $mathrm{Spec}(mathcal A)$ of the supercommutative superalgebra $mathcal A$ which may be described as the zero locus of an ideal $J subseteq mathcal A$ is simply the spectrum of the supercommutative superalgebra $frac{mathcal A}{J}$. We have a canonical morphism $mathrm{Spec} left (frac{mathcal A}{J} right ) to mathrm{Spec}(mathcal A)$. This construction doesn't seem to easily generalize to supermanifolds.
differential-geometry algebraic-geometry superalgebra supermanifolds supergeometry
asked Nov 17 at 10:52
Blazej
1,474618
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I would like to in what sense supermanifolds may be defined by systems of equations in the ordinary flat superspace. I am particularly interested in the approach to supergeometry via ringed spaces.
Remark: situation is quite clear for me in the case of affine super schemes. In this case subscheme of the spectrum $mathrm{Spec}(mathcal A)$ of the supercommutative superalgebra $mathcal A$ which may be described as the zero locus of an ideal $J subseteq mathcal A$ is simply the spectrum of the supercommutative superalgebra $frac{mathcal A}{J}$. We have a canonical morphism $mathrm{Spec} left (frac{mathcal A}{J} right ) to mathrm{Spec}(mathcal A)$. This construction doesn't seem to easily generalize to supermanifolds.
differential-geometry algebraic-geometry superalgebra supermanifolds supergeometry
asked Nov 17 at 10:52
Blazej
1,474618
I would like to in what sense supermanifolds may be defined by systems of equations in the ordinary flat superspace. I am particularly interested in the approach to supergeometry via ringed spaces.
Remark: situation is quite clear for me in the case of affine super schemes. In this case subscheme of the spectrum $mathrm{Spec}(mathcal A)$ of the supercommutative superalgebra $mathcal A$ which may be described as the zero locus of an ideal $J subseteq mathcal A$ is simply the spectrum of the supercommutative superalgebra $frac{mathcal A}{J}$. We have a canonical morphism $mathrm{Spec} left (frac{mathcal A}{J} right ) to mathrm{Spec}(mathcal A)$. This construction doesn't seem to easily generalize to supermanifolds.
differential-geometry algebraic-geometry superalgebra supermanifolds supergeometry
differential-geometry algebraic-geometry superalgebra supermanifolds supergeometry
asked Nov 17 at 10:52
Blazej
1,474618
asked Nov 17 at 10:52
Blazej
1,474618
asked Nov 17 at 10:52
Blazej
1,474618
asked Nov 17 at 10:52
Blazej
1,474618
asked Nov 17 at 10:52
Blazej
1,474618
1,474618
add a comment |
add a comment |
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