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The pillowcase orbifold is the 2-dimensional flat (complex) orbifold which is the global quotient of the torus by the reflection involution :
The Weierstrass elliptic function , regarded as a holomorphic function with values in the Riemann sphere , exhibits the coarse underlying topological space of the pillowcase orbifold as the 2-sphere:
(e.g Mukase 2004, end of §1.4, Eskin & Okounkov 2005, p. 1, Goujard & Moeller 2018, §2.3)
spindle orbifold][## References ### General * [[Alex Eskin]?, Andrei Okounkov, Pillowcases and quasimodular forms, In: Ginzburg V. (ed.) Algebraic Geometry and Number Theory, Progress in Mathematics 253 Birkhäuser (2006) [arXiv:math/0505545, doi:10.1007/978-0-8176-4532-8_1]
Elise Goujard, Martin Moeller, Pillowcase covers: Counting Feynman-like graphs associated with quadratic differentials [arXiv:1809.05016]
On fluxed KK-compactification of D=6 supergravity on pillowcase orbifold fibers:
Christoph Ludeling, 6D supergravity: Warped solution and gravity mediated supersymmetry breaking, PhD thesis, Hamburg (2006) [doi:10.3204/DESY-THESIS-2006-020]
Gero von Gersdorff, Anomalies on Six Dimensional Orbifolds, JHEP 0703:083 (2007) [arXiv:hep-th/0612212]
Markus Dierigl, Aspects of Six-Dimensional Flux Compactifications, PhD thesis, Hamburg (2017) [doi:10.3204/PUBDB-2017-09253]
and in the broader context of non-supersymmetric flat orbifolds of supergravity theories:
Last revised on May 11, 2024 at 08:54:46. See the history of this page for a list of all contributions to it.