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**3**

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**1**answer

95 views

### The volume of a region arising from planar linkages

Let $x_0,\dots,x_n$ be a collection of variable points in $\mathbb{R}^2$ and let $c>0$ be a fixed constant. Is there any way I could compute an upper bound of the volume of the region in $\mathbb{...

**1**

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90 views

### Obstruction to Gorenstein Liaisons of space curves

Let $P_1,P$ be Hilbert polynomials of curves in $\mathbb{P}^3$. Denote by $H_{P_1,P}$ the flag Hilbert scheme parametrizing pairs $(C_1 \subset C)$ where $C_1, C$ are of Hilbert polynomials $P_1$ and $...

**2**

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75 views

### A basic question on complete intersection liaisons of curves

I am a beginner in the Linkage theory and would like to clarify certain points I am not sure of.
Let $P$ be the Hilbert polynomial of a curve in $\mathbb{P}^3$. Let $L$ be an irreducible component of ...

**4**

votes

**1**answer

327 views

### A.J. Galitzer's Ph.D. thesis: On the moduli space of closed polygonal linkages on the 2-sphere

Recently I became curious about moduli spaces of linkages and so I found and began reading some papers of Kapovich and Millson. In the paper Hodge theory and the art of paper folding, the Ph.D. ...

**6**

votes

**2**answers

338 views

### Calabi-Yau manifolds and polygonal linkage configuration spaces: related?

I was reading about Calabi-Yau manifolds, about which I know little, and was wondering
if these (or related complex manifolds, perhaps K3 surfaces) can be viewed as configuration
spaces (or moduli ...

**2**

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**0**answers

144 views

### When is the area of the convex hull of a tree-like linkage maximal?

This is inspired from this recent question. Given in the plane a tree-linkage (fixed length rigid edges, vertices are flexible joints, connected and no cycles) is there a simple description of when ...

**10**

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**5**answers

423 views

### Is the area of a polygonal linkage maximized by having all vertices on a circle?

Consider a (non-stellated) polygon in the plane. Imagine that the edges are rigid, but that the vertices consist of flexible joints. That is, one is allowed to move the polygon around in such a way ...