The analytic-geometry tag has no wiki summary.
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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 ...
2
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1answer
125 views
Tangent cone and embedded components
Is it possible for a reduced, equidimensional germ of complex analytic singularity to have a tangent cone with embedded components but without multiple irreducible components?
If it is, how can you ...
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2answers
290 views
supporting facts to fujita conjecture
I came across the Fujita conjecture which is perhaps very widely known. I want to know what are the supporting facts to the truth of the conjecture.
http://en.wikipedia.org/wiki/Fujita_conjecture
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Asymptotics vs Puiseux series
Define asymptotic as a class of sequences {$ x_i$},$_{i\in\mathbb N}$ modulo equivalence {$x_i$}={$y_i$} if $\lim_{i\to\infty} (x_i/y_i)=c\in\mathbb R,c\ne 0$.
More, we define $X= \{x_i\} \lt Y= \{ ...
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On Determinants of Laplacians on Riemann Surfaces
History of the Formula: In their famous paper "On Determinants of Laplacians on Riemann Surfaces" (1986), D'Hoker and Phong computed the determinant of the Laplacian $\Delta_n^+$ on the space $T^n$ of ...
2
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3answers
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How to tell if a second-order curve goes below the $x$ axis?
Suppose we have a second-order curve in general form:
(1) $a_{11}x^{2}+2a_{12}xy+a_{22}y^{2}+2a_{13}x+2a_{23}y+a_{33}=0$.
I'd like to know if there is a simple condition that ensures that the curve ...
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120 views
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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Topology of theta nulls
Siegel upper half-space, $\mathfrak{h}_g$, consists of symmetric $g\times g$ complex matrices with positive-definite imaginary part. From an element $Z\in \mathfrak{h}_g$ we can construct a theta ...
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498 views
Geometric realization of Hochschild complex
Let $A$ be a commutative $\mathbb{C}$-algebra, and consider $C_{\bullet}(A,A)$ the simplicial Hochschild homology module of $A$ with respect to itself (i.e. $C_{n}(A,A)=A^{\otimes (n+1)}$). This is a ...
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Cohesive ∞-toposes for analytic geometry
There is a class of big ∞-toposes that come with a good supply of intrinsic notions of differential geometry and differential cohomology: called cohesive ∞-toposes (after Lawvere's cohesive toposes).
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592 views
Lattice points close to a line
Take a sheet of grid paper and draw a straight line in any direction from the origin. What is the closest non-zero grid point $\boldsymbol{p}\in\mathbb{Z}^2$ within a distance $\epsilon>0$ of the ...
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1answer
352 views
Pathologies of analytic (non-algebraic) varieties.
Note: By an "analytic non-algebraic" surface below I mean a two dimensional compact analytic variety $X$ (over $\mathbb{C}$) which is not an algebraic variety.
A property of Nagata's example (see ...
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2answers
313 views
If $K$ and $L$ are compact convex sets with smooth boundary, does their union have piecewise-smooth boundary?
Clarification: by "piecewise", I mean a finite number of pieces.
I'm sure this must be true, but my search for a citation was in vain (although I did learn the new term "polyconvex").
Thanks!
2
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1answer
202 views
Is a compact subset of a Stein space admitting a fundamental system of Stein neighbourhoods necessarily holomorphically convex?
Let X be a Stein manifold and let K be a compact subset of X. Suppose that K possesses in X a fundamental system of neighbourhoods which are Stein spaces. Then, it is a result by Rossi that such a ...
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1answer
262 views
Is the closure of an open holomorphically convex subset of a Stein space holomorphically convex?
Let X be a Stein manifold and U an open, connected, relatively compact, holomorphically convex subset of X. Is the closure of U in X holomorphically convex?
Also, if X is a Stein space with a finite ...
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658 views
Generalized GAGA
So, I have heard GAGA works for Rigid Analytic spaces. I know next to nothing about this, but it made me curious as to whether there are any other contexts in which GAGA "works". Of course, this is a ...
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1answer
710 views
Are flat morphisms of analytic spaces open?
Let $f:X\to Y$ be a morphism of complex analytic spaces. Assume $f$ is flat (or, more generally, that there is a coherent sheaf on $X$ with support $X$ which is $f$-flat). Is $f$ an open map?
The ...
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2answers
620 views
Embeddings and triangulations of real analytic varieties
This is a follow up question to my answer here How do you define the Euler Characteristic of a scheme?
A real analytic space is a ringed space locally isomorphic to $(X,O/I)$ where $X$ is the zero ...
