A note on Todorov surfaces
نویسنده
چکیده
Let S be a Todorov surface, i.e., a minimal smooth surface of general type with q = 0 and pg = 1 having an involution i such that S/i is birational to a K3 surface and such that the bicanonical map of S is composed with i. The main result of this paper is that, if P is the minimal smooth model of S/i, then P is the minimal desingularization of a double cover of P ramified over two cubics. Furthermore it is also shown that, given a Todorov surface S, it is possible to construct Todorov surfaces Sj with K = 1, . . . , K S − 1 and such that P is also the smooth minimal model of Sj/ij , where ij is the involution of Sj . Some examples are also given, namely an example different from the examples presented by Todorov in [To2]. 2000 Mathematics Classification: 14J29, 14J28.
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