Spaces of conics on low degree complete intersections

Pan, Xuanyu

doi:10.1090/tran/7107

Spaces of conics on low degree complete intersections
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by Xuanyu Pan PDF

Trans. Amer. Math. Soc. 370 (2018), 5381-5400 Request permission

Abstract:

Let $X$ be a smooth complete intersection contained in $\mathbb {P}^n_{\mathbb {C}}$ and of low degree. We consider conics contained in $X$ and passing through two general points of $X$. We show that the moduli space of these conics is a smooth complete intersection in a projective space. The main ingredients of the proof are a criterion for characterizing when a smooth projective variety is a complete intersection in a projective space, the Grothendieck-Riemann-Roch theorem, and the geometry of spaces of conics.

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