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تسجيل مستخدم جديدGlobal Prym-Torelli for double coverings ramified in at least 6 points
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We prove that the ramified Prym map $mathcal P_{g, r}$ which sends a covering $pi:Dlongrightarrow C$ ramified in $r$ points to the Prym variety $P(pi):=text{Ker}(text{Nm}_{pi})$ is an embedding for all $rge 6$ and for all $g(C)>0$. Moreover, by studying the restriction to the locus of coverings of hyperelliptic curves, we show that $mathcal P_{g, 2}$ and $mathcal P_{g, 4}$ have positive dimensional fibers.
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In this paper we consider the Prym map for double coverings of curves of genus $g$ ramified at $r>0$ points. That is, the map associating to a double ramified covering its Prym variety. The generic Torelli theorem states that the Prym map is generica
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