The Picard group of the moduli of smooth complete intersections of two quadrics

Asgarli, Shamil; Inchiostro, Giovanni

doi:10.1090/tran/7732

The Picard group of the moduli of smooth complete intersections of two quadrics
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by Shamil Asgarli and Giovanni Inchiostro PDF

Trans. Amer. Math. Soc. 372 (2019), 3319-3346 Request permission

Abstract:

We study the moduli space of smooth complete intersections of two quadrics in $\mathbb {P}^n$ by relating it to the geometry of the singular members of the corresponding pencils. By giving an alternative presentation for the moduli space of complete intersections, we compute the Picard group for all $n\geq 3$.

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