Computation of the openness of some loci of modules

Rossi, Fabio; Spangher, Walter

doi:10.1007/3-540-54522-0_127

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Lemma 2 Let Us Denote By γ P the Lines Of γ Through P; Then1

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2008

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“…a parasitical line. The ideal sheaf I X has a minimal free resolution of the form 20) and the points where X is not Cohen-Macaulay are the ones defined by the first nonzero Fitting ideal of A, where A is the matrix appearing in (20) (see for example [27]). As an explicit example, let us take H = V ( p 05 + p 12 + p 14 + p 34 ) so the quadric Q, component of the cubic surface Y , has equation a 2 + b 2 + c 2 + d 2 − ac, i.e.…”

Section: Lemma 2 Let Us Denote By γ P the Lines Of γ Through P; Thenmentioning

confidence: 99%

Congruences of lines in $${{\mathbb P}^5}$$ , quadratic normality, and completely exceptional Monge–Ampère equations

Poi

Mezzetti

2008

Geom Dedicata

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The existence is proved of two new families of sextic threefolds in P 5 , which are not quadratically normal. These threefolds arise naturally in the realm of first order congruences of lines as focal loci and in the study of the completely exceptional Monge-Ampère equations. One of these families comes from a smooth congruence of multidegree (1, 3, 3) which is a smooth Fano fourfold of index two and genus 9.

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Section: Lemma 2 Let Us Denote By γ P the Lines Of γ Through P; Thenmentioning

confidence: 99%