Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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PROJECTIONS OF ALGEBRAIC VARIETIES WITH ALMOST LINEAR PRESENTATION II

  • Ahn, Jeaman (Department of Mathematics Education Kongju National University)
  • Received : 2021.03.16
  • Accepted : 2021.05.08
  • Published : 2021.05.15
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Abstract

Let X be a nondegenerate reduced closed subscheme in ℙn. Assume that πq : X → Y = πq(X) ⊂ ℙn-1 is a generic projection from the center q ∈ Sec(X) \ X where Sec(X) = ℙn. Let Z be the singular locus of the projection πq(X) ⊂ ℙn-1. Suppose that IX has the almost minimal presentation, which is of the form R(-3)β2,1 ⊕ R(-4) → R(-2)β1,1 → IX → 0. In this paper, we prove the followings: (a) Z is either a linear space or a quadric hypersurface in a linear subspace; (b) $H^1({\mathcal{I}_X(k)})=H^1({\mathcal{I}_Y(k)})$ for all k ∈ ℤ; (c) reg(Y) ≤ max{reg(X), 4}; (d) Y is cut out by at most quartic hypersurfaces.

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Acknowledgement

The author was supported by the research grant of the Kongju National University for the research year in 2018-2019.

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