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- W2950294501 abstract "We show that the moduli space of elliptic curves of minimal degree in a general Fano variety of lines of a cubic fourfold is a non-singular curve of genus $631$. The curve admits a natural involution with connected quotient. We find that the general Fano contains precisely $3780$ elliptic curves of minimal degree with fixed (general) $j$-invariant. More generally, we express (modulo a transversality result) the enumerative count of elliptic curves of minimal degree in hyper-Kahler varieties with fixed $j$-invariant in terms of Gromov--Witten invariants. In $K3[2]$-type this leads to explicit formulas of these counts in terms of modular forms." @default.
- W2950294501 created "2019-06-27" @default.
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- W2950294501 date "2019-06-13" @default.
- W2950294501 modified "2023-09-27" @default.
- W2950294501 title "Elliptic curves in hyper-Kahler varieties" @default.
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