Twelve Rational curves on Enriques surfaces

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چکیده

Abstract Given $$d\in {\mathbb {N}}$$ d ? N , we prove that any polarized Enriques surface (over field k of characteristic $$p \ne 2$$ p ? 2 or with a smooth K3 cover) degree greater than $$12d^2$$ 12 contains at most 12 rational curves d . For $$d>2$$ > construct examples surfaces high contain exactly degree- curves.

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ژورنال

عنوان ژورنال: Research in the Mathematical Sciences

سال: 2021

ISSN: ['2522-0144', '2197-9847']

DOI: https://doi.org/10.1007/s40687-021-00262-7