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In geometric computer vision the trifocal tensors are 3×3×3 tensors T by whose means three different camera views of the same scene are related to each other. In this paper we find two different sets of constraints, in the entries of T, that must be satisfied by trifocal tensors. The first set gives exactly the (closure of the) trifocal locus, i.e. all… (More)
We define the monomial invariants of a projective variety Z; they are invariants coming from the generic initial ideal of Z. Using this notion, we generalize a result of Cook [C]: If Z is an integral variety of codimension two, satisfying the additional hypothesis sZ = sΓ, then its monomial invariants are connected.
A vanishing theorem for numerically connected divisors, first given by Bombieri for surfaces, is established in any dimension. A definition of k-connected divisors is proposed, then such divisors on threefolds are studied.
Let X be a compact Kähler manifold, and let L be a line bundle on X. When L = K X is the canonical bundle, the map ρ computes a second fundamental form associated to the deformations of X. If X = C is a curve, then ρ is a lifting of the Wahl map I 2 (L) → H 0 (L 2 ⊗ K 2 C). We also show how to generalize the construction of ρ to the cases of harmonic… (More)