Questions tagged [analytic-geometry]
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Dimensions of fibers of analytic map
I must admit that I know nothing about p-adic geometry, so the following question may be completely trivial.
Let $V\subset K^n$ be an affine algebraic variety. Let $D$ be a polydisk, and $F$ be an ...
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Pascal and Brianchon's theorems generalized for hyperbolic paraboloid
I know that giving a general version of these two theorems for quadrics can be quite tricky, but if we restrict ourselves to a verssion that holds for the hyperbolic paraboloid only it should be ...
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The intersection number $C\cdot D=\deg(D_{/C})$
Let $S$ be an algebraic complex surface, and $D=[(U_\alpha,f_{\alpha})]$ is a Cartier divisor over $S$, and let $\cal{O}_S(D)$ be the sheaf associated to $D$. And let $C$ be a complex compact curve in ...
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Some questions related to the unitary operators
A unitary operator is a surjective linear operator between complex inner product spaces, which preserves the inner product.
What is the name of the analogue for the real case? Orthogonal operator ...
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Reference request: Oldest books on analytic geometry with unsolved exercises?
Per the title, what are some of the oldest books on analytic geometry out there with unsolved exercises? Maybe there are some hidden gems from before the 20th century out there.
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Can an analytic set admit such a foliation?
I confess to be not an expert of analytic geometry, but I have come across the following problem, for which I need an help from experts in this specific field.
I was wondering myself if it is ...
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On the number of integral points of analytic curves
Consider a curve over some number field $\mathbb{K}$. By Falting's Theorem, if the genus $g$ is greater than $1$, the curve has only finitely many integral points. Moreover, as shown in Bilu, Y. et al....
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Good covering of a (singular) curve in a complex surface
Let $W$ be a $2$-dimensional complex manifold and $C\subset W$ a compact complex curve (possibly singular). I would like to know a reference for the following fact: there exists a collection $\{V_j\}...
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Asymptotes of hyperbolic sections of a given cone
A book I'm reading (Companion to Concrete Math Vol. I by Melzak) mentions, "...any ellipse occurs as a plane section of any given cone. This is not the case with hyperbolas: for a fixed cone only ...
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Define this set of power curves bounded above by a given geometric curve and below by y = 1
Let $f(x) = 1/(1-x)$, with $x$ a real number in $[0, 1]$ and $f(x)$ a real number in $[1, \infty]$. This is clearly part of a geometric curve, as well as part of a branch of a hyperbola with ...
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Conformal map from a 7-sided polyhedron to a square pyramid
I have a right-angled square pyramid, $A$, whose height and base-length are $l$. By 'right-angled', I mean that the apex of $A$ lies vertically above one of the vertices in its base. Now supposed I ...
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