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- W2946102904 abstract "We discuss the Borisov-Nuer conjecture in connection with the canonical maps from the moduli spaces $mathcal M_{En,h}^a$of polarized Enriques surfaces with fixed polarization type $h$ to the moduli space $mathcal F_g$ of polarized $K3$ surfaces of genus $g$ with $g=h^2+1$, and we exhibit a naturally defined locus $Sigma_gsubsetmathcal F_g$. One direct consequence of the Borisov-Nuer conjecture is that $Sigma_g$ would be contained in a particular Noether-Lefschetz divisor in $mathcal F_g$, which we call the Borisov-Nuer divisor and we denote by $mathcal{BN}_g$. In this short note, we prove that $Sigma_gcapmathcal{BN}_g$ is non-empty whenever $(g-1)$ is divisible by $4$. To this end, we construct polarized Enriques surfaces $(Y, H_Y)$, with $H_Y^2$ divisible by $4$, which verify the conjecture. In particular, the conjecture holds also for any element $mathcal M_{En,h}^a$, if $h^2$ is divisible by $4$ and $h$ is the same type of polarization." @default.
- W2946102904 created "2019-05-29" @default.
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- W2946102904 date "2019-05-23" @default.
- W2946102904 modified "2023-09-26" @default.
- W2946102904 title "On the Borisov-Nuer conjecture and the image of the Enriques-to-K3 map" @default.
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- W2946102904 doi "https://doi.org/10.48550/arxiv.1905.09623" @default.
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