Abstract
Let S be an Enriques surface over an algebraically closed field k of arbitrary characteristic p. Recall that this means that S is a connected smooth projective surface whose canonical class is numerically trivial and second Betti number equal to 10 [4]. It is well-known that, generically over k=(E, an Enriques surface does not contain nonsingular rational curves. This can be seen, for example, by considering the period space for such surfaces I-3]. Also, it is known that if S contains such a curve, then, again generically, it contains infinitely many of them. This can be seen, for example, by viewing an Enriques surface as an elliptic surface whose jacobian surface is a rational elliptic surface. Assuming that the latter is general enough, its translation group is infinite and acts on S by automorphisms. Thus, the existence of one such curve implies the existence of infinitely many. In this paper we prove the following rather surprising result:
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
