Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Apisa, Paul"'
Autor:
Apisa, Paul
We give a new short proof of the classification of rank at least two invariant subvarieties in genus three, which is due to Aulicino, Nguyen, and Wright. The proof uses techniques developed in recent work of Apisa and Wright.
Comment: 9 pages, 2
Comment: 9 pages, 2
Externí odkaz:
http://arxiv.org/abs/2409.07603
Autor:
Apisa, Paul, Aulicino, David
We show that the only algebraically primitive invariant subvarieties of strata of translation surfaces with quadratic field of definition are the decagon, Weierstrass curves, and eigenform loci in genus two and the rank two example in the minimal str
Externí odkaz:
http://arxiv.org/abs/2404.10273
Autor:
Apisa, Paul
We introduce a construction of affine invariant subvarieties in strata of translation surfaces whose input is purely combinatorial. We then show that this construction can be used to construct the Bouw-Moeller Teichmueller curves and the seven Eskin-
Externí odkaz:
http://arxiv.org/abs/2310.13776
We construct moduli spaces of complex affine and dilation surfaces. Using ideas of Veech, we show that the the moduli space of affine surfaces with fixed genus and with cone points of fixed complex order is a holomorphic affine bundle over the moduli
Externí odkaz:
http://arxiv.org/abs/2204.05257
Autor:
Apisa, Paul
The orbit closure of the unfolding of every rational right and isosceles triangle is computed and the asymptotic number of periodic billiard trajectories in these triangles is deduced. This follows by classifying all orbit closures of rank at least t
Externí odkaz:
http://arxiv.org/abs/2110.07540
Autor:
Apisa, Paul
We classify the GL(2,R)-invariant subvarieties M in strata of Abelian differentials for which any two M-parallel cylinders have homologous core curves. This answers a question of Mirzakhani and Wright. As a corollary we show that outside of an explic
Externí odkaz:
http://arxiv.org/abs/2103.02133
Autor:
Apisa, Paul, Wright, Alex
We classify GL(2,R) orbit closures of translation surfaces of rank at least half the genus plus 1.
Comment: Comments welcome
Comment: Comments welcome
Externí odkaz:
http://arxiv.org/abs/2102.06567
Autor:
Apisa, Paul, Wright, Alex
We classify a natural collection of GL(2,R)-invariant subvarieties, which includes loci of double covers, the orbits of the Eierlegende-Wollmilchsau, Ornithorynque, and Matheus-Yoccoz surfaces, and loci appearing naturally in the study of the complex
Externí odkaz:
http://arxiv.org/abs/2011.09452
Autor:
Apisa, Paul, Wright, Alex
We introduce and study diamonds of GL(2,R)-invariant subvarieties of Abelian and quadratic differentials, which allow us to recover information on an invariant subvariety by simultaneously considering two degenerations, and which provide a new tool f
Externí odkaz:
http://arxiv.org/abs/2011.08807