Cylinder decomposition veech surface
WebA cylinder diagram encodes the combinatorics of cylinder decomposition of a completely periodic direction in a translation surface. If we adjoin coordinates to this combinatorial datum, we have a complete description of the underlying surface. In the case of arithmetic curves, the coordinates can be taken to be rational numbers. http://homepages.math.uic.edu/~masur/chm-rv.pdf
Cylinder decomposition veech surface
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WebDec 19, 2016 · Theorem 1.1. Let S be a Veech surface in 7i(2) which cannot be rescaled so that p(Hi(S,Z)) cQxQ. Let v be a completely periodic direction for S. Suppose the cylinder decompositon in the direction v has two cylinders. Let Wi,w2,hi,h2,ti,t2 be the widths, heights and twists of these two cylinders. The twists are measured WebDec 19, 2016 · the direction v, the surface decomposes as a union of cylinders. A surface S is completely periodic if any direction in which there is at least one cylinder of closed …
WebVEECH SURFACES AND THEIR PERIODIC POINTS 179 Theorem 1.4. Let (X,u) be an non-arithmetic Veech surface such that X is of type (g,n). For every holomorphic family of Riemann surfaces constructed from the Veech group … http://www-personal.umich.edu/~alexmw/Cylinder.pdf
WebAug 17, 2004 · the direction v, the surface decomposes as a union of cylinders. A surface S is completely periodic if any direction in which there is at least one cylinder of closed … WebDepartment of Mathematics The University of Chicago
WebMore precisely, regular n-gon surfaces have (n, ∞, ∞)-triangle groups as Veech groups, while the Veech groups of Bouw-Möller surfaces are (m, n, ∞)-triangle groups for m and n not both even ...
Webcore(X) decomposes into a (maybe empty) family of cylinders of commensurablemoduli. Otherwise,theSL(2,R)-orbitof(X,q) isnotclosedintheambientstratum. ... In strata of dimension one, the Veech group of ev-ery surface is of continuous type. In strata of dimension at least three, the Veech group of a generic surface is trivial. In strata of ... ircc publicationsWebA Veech surface is arithmeticif it is a covering of a flat torus, ramified over one point; otherwise, it is a non-arithmetic Veech surface. 2.2. Classification of Veech surfaces … ircc r183WebA Veech surface (X,q) is called primitive if it cannot be realized as a branched cover over (X′,q′), where the genus of X′ is lower than the genus of X and the quadratic differential q′ pulls back to q under the covering map. If (X,q) is a Veech surface that is not primitive, then the corresponding surface (X′,q′) is also Veech ircc public accountsWebThe height of the cylinder is the width W W of the rectangular label. So the area of the label can be represented as. To find the total surface area of the cylinder, we add the areas … ircc r182WebA cylinder decomposition of (X,A) is a collection of maximal cylinders in (X,A) so that the closures of the cylinders in Xcover Xand so that each two cylinders are disjoint. We … ircc r10WebThe Veech group of the surface is the subgroup of SL(2,R) consisting of elements that map the surface to itself by this action. I will describe a method for computing elements of the Veech group. ... • A multi-curve on a surface produces a decomposition of the surface into cylinders. Thus a parabolic automorphism of the surface may be ... ircc publications and manualsWebThe trace eld of a Veech surface (X;!) is Q(tr A : A 2SL(X;!)) is the smallest eld extension of Q that contains the trace of all elements of SL(X;!). 1 For an appropriately scaled … order copy of birth certificate kentucky