Regular Cyclic Coverings of the Platonic Maps
نویسندگان
چکیده
منابع مشابه
Regular Cyclic Coverings of the Platonic Maps
The Möbius-Kantor map {4 + 4, 3} [CMo, §8.8, 8.9] is a regular orientable map of type {8, 3} and genus 2. It is a 2-sheeted covering of the cube {4, 3}, branched over the centers of its six faces, each of which lifts to an octagonal face. Its (orientation-preserving) automorphism group is isomorphic to GL2(3), a double covering of the automorphism group PGL2(3) ∼= S4 of the cube. The aim of thi...
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A Platonic map is a regular map M on the sphere S. Following [CMo] we say that M has type {n,m} if it has n-gonal faces and the vertices have valency m; since these parameters determine a Platonic map uniquely, one can unambiguously write M = {n,m}. As one must have 0 ≤ (m − 2)(n − 2) < 4, there are precisely the possibilities M = {n, 2} (dihedron), M = {2,m} (hosohedron), M = {3, 3} (tetrahedr...
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The regular coverings of regular affine algebraic maps are considered, and a large family of totally ramified coverings—the so-called Steinberg and Accola coverings—are fully classified.
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Prym Varieties of Cyclic Coverings
The Prym map of type (g, n, r) associates to every cyclic covering of degree n of a curve of genus g, ramified at a reduced divisor of degree r, the corresponding Prym variety. We show that the corresponding map of moduli spaces is generically finite in most cases. From this we deduce the dimension of the image of the Prym map.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2000
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0332