LShapedSurfaces < WildSurfaces

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WildSurfaces.LShapedSurfacesr1.1 - 08 Feb 2006 - 10:14 - ThierryMonteiltopic end

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L-shaped translation surfaces

Description of the surface

It is in fact a familiy of surfaces P(a,b) that depend on two parameters:

The opposite lines are identified by translation.

Basic facts

genus : 2
stratum : H(2)
Veech group :

Some Properties

Lattice property

P(a,b) is a Veech surface if and only if

$( (a,b) \in \mathbb{Q}^2 ) \ \mbox{ or } \ ( \exists (x,y,z,d) \in \mathbb{Q}^3 \times \mathbb{N} \ \ (x+y=1 \mbox{ and } a=x+z\sqrt{d} \mbox{ and } b=y+z\sqrt{d} ))$

finite blocking property

P(a,b) has the FiniteBlockingProperty if and only if $(a,b) \in \mathbb{Q}^2$

References

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I	Attachment	Action	Size	Date	Who	Comment
	Pab.png	manage	2.7 K	08 Feb 2006 - 10:39	ThierryMonteil
	Pab.fig	manage	0.4 K	08 Feb 2006 - 10:38	ThierryMonteil

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