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 Civic Duty
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11h
revised Use of discriminent in proving that the points of unramification is open…
added 30 characters in body
1d
asked Use of discriminent in proving that the points of unramification is open…
1d
comment Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
@Mohan which is 1 iff it gives a local equation?
1d
comment Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
@Mohan For the second sentance, I forgot to say that I want to compute the divisor associated to a regular function by computing intersection multiplicities.
1d
comment Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
@Mohan So, a local equation would be any curve that intersects with multiplicity one? Does this mean I can bypass the local equation > valuation computation, and simply compute the intersection multiplcity of the hypersurface defined by my function and the curve at the point p? This is done by computing the k dimension of the tensor product over the affine coordinate ring?
1d
comment Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
@Mohan Makes sense, thanks.
1d
comment Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
@Mohan So how do I find local equations? For instance if I want to compute the divisor of some rational function, I need the local equation to compute the valuation...
1d
comment Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
@Mohan Oh ... Now I see the problem with looking at the world with non-schemey eyes.
2d
accepted Diffeomorphism that pulls back the curvature tensor is an isometry?
2d
comment Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
@user40276 What do you mean by the equation having second order derivatives? The local equation? But it isn't unique, isn't it? I'm still confused. Can you give an example where the equation of the tangent line won't cut out the point $p$ locally? (I mean, the tangent line is going to intersect the curve at finitely many points, so there is a neighborhood where it cuts out that point. Is there something wrong with multiplicity?)
2d
comment Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
(I think in general it is something that can be asked about codimension 1 subvarieties...)
2d
revised Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
edited body
2d
comment Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
@Mohan Yes, the ns are distinct. A mean a generator for the maximal ideal in the local ring at x, or (I think) equivalently, a function regular in some neighborhood that cuts out x (in that nbhd).
2d
comment Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
@user40276 I read the pages - I'm not asking about an equation for tangent plane, but for the point p. (Local equation of a subvariety.) I don't see the connection, but the book is certainly nice.
2d
comment Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
@user40276 Unfortunately I don't have access to that book.
2d
comment Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
@user40276 Can you expand on your answer a little?
2d
asked Is a local equation for a smooth point on a curve given by the equation for the “tangent line”?
Aug
24
asked Explicit constructions of Haar measures?
Aug
23
awarded  Civic Duty
Aug
23
answered Constant rank theorem: intuition?