We consider the space Rg,S3S3 of curves with a connected S3-cover, proving that for any odd genus g≥13 this moduli is of general type. Furthermore we develop a set of tools that are essential in ...approaching the case of G-covers for any finite group G.
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Using the notion of a root datum of a reductive group G we propose a tropical analogue of a principal G-bundle on a metric graph. We focus on the case G=GLn, i.e. the case of vector bundles. Here we ...give a characterization of vector bundles in terms of multidivisors and use this description to prove analogues of the Weil–Riemann–Roch theorem and the Narasimhan–Seshadri correspondence. We proceed by studying the process of tropicalization. In particular, we show that the non-Archimedean skeleton of the moduli space of semistable vector bundles on a Tate curve is isomorphic to a certain component of the moduli space of semistable tropical vector bundles on its dual metric graph.
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Essentially finite G-torsors Ghiasabadi, Archia; Reppen, Stefan
Bulletin des sciences mathématiques,
11/2023, Letnik:
188
Journal Article
Recenzirano
Odprti dostop
Let X be a smooth projective curve of genus g, defined over an algebraically closed field k, and let G be a connected reductive group over k. We say that a G-torsor is essentially finite if it admits ...a reduction to a finite group, generalising the notion of essentially finite vector bundles to arbitrary groups G. We give a Tannakian interpretation of such torsors, and we prove that all essentially finite G-torsors have torsion degree, and that the degree is 0 if X is an elliptic curve. We then study the density of the set of k-points of essentially finite G-torsors of degree 0, denoted MGef,0, inside MGss,0, the k-points of all semistable degree 0 G-torsors. We show that when g=1, MGef⊂MGss,0 is dense. When g>1 and when char(k)=0, we show that for any reductive group of semisimple rank 1, MGef,0⊂MGss,0 is not dense.
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