On the Multiplicative Structure of the Rao Module of Space Curves Lying on a Smooth Quadric

Giuffrida, Sergio; Maggioni, Renato

doi:10.1081/agb-120003478

Cited by 3 publications

(8 citation statements)

References 6 publications

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“…Notice that the fact that the map (3) has maximal rank in the case of n = m = 1 helps understanding the multiplicative stucture of the bigraded module H 1 * O Q , and hence that of the Rao module of curves C ⊂ Q when Q is embedded in P 3 , cfr. [1].…”

Section: Problem 13 Consider the Multiplication Mapmentioning

confidence: 95%

“…For instance the equivalence of Problem 1.1 and Problem 1.3 is due to the fact that (1) and W = H 0 O P n (1), by Künneth formula and Serre duality. Moreover the multiplication…”

Section: Problem 13 Consider the Multiplication Mapmentioning

confidence: 96%

“…Recall that Pic(Q) ∼ = Z × Z, with basis O Q (1, 0) = π * 1 O P m (1) and O Q (0, 1) = π * 2 O P n (1). In these notations, one may consider the following third version of Problem 1.1.…”

Section: Is This Map Of Maximal Rank If D Is Sufficiently General Inmentioning

confidence: 98%

“…1 We set γ = max(α,α) and δ = max(β,β). Consider the sub-grid G γ,δ = {P i, j : 1 ≤ i ≤ γ + 1, 1 ≤ j ≤ δ + 1}.…”

Section: Lemma 31 There Exists a Subset Z ⊂ G Such Thatmentioning

confidence: 99%

See 3 more Smart Citations

Multiplications of maximal rank in the cohomology of $${\mathbb{P}^1\times \mathbb{P}^1}$$

Giuffrida¹,

Maggioni²,

Re³

2010

Collect. Math.

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Let Q = P 1 × P 1 and let C ⊆ Q be a curve of type (a, b) having equation F = 0. The main purpose of this paper is to analize the multiplicative structure of the bi-graded module H 1 * O Q , in particular to prove that for any r, s ≥ 0 the multiplication mapinduced by F has maximal rank for the general C of type (a, b). Interpretations of this problem in the contexts of multilinear algebra and differential algebra are emphasized.

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Section: Problem 13 Consider the Multiplication Mapmentioning

confidence: 95%

“…For instance the equivalence of Problem 1.1 and Problem 1.3 is due to the fact that (1) and W = H 0 O P n (1), by Künneth formula and Serre duality. Moreover the multiplication…”

Section: Problem 13 Consider the Multiplication Mapmentioning

confidence: 96%

Section: Is This Map Of Maximal Rank If D Is Sufficiently General Inmentioning

confidence: 98%

“…1 We set γ = max(α,α) and δ = max(β,β). Consider the sub-grid G γ,δ = {P i, j : 1 ≤ i ≤ γ + 1, 1 ≤ j ≤ δ + 1}.…”

Section: Lemma 31 There Exists a Subset Z ⊂ G Such Thatmentioning

confidence: 99%

See 2 more Smart Citations

Multiplications of maximal rank in the cohomology of $${\mathbb{P}^1\times \mathbb{P}^1}$$

Giuffrida¹,

Maggioni²,

Re³

2010

Collect. Math.

Self Cite

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“…In a previous paper [6] we considered the problem of describing the multiplicative structure of the Rao module M(C) = H 1 * (P 3 , I C ) = n≥0 M n of a curve C lying on a smooth quadric Q ⊆ P 3 . This means to give, for any form Γ of degree m, the rank of the linear map "product by Γ "…”

Section: Introductionmentioning

confidence: 99%

Hankel planes

Giuffrida

Maggioni

2007

Journal of Pure and Applied Algebra

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Starting from an (m +1)×(n +1) matrix A one can construct (m + p+1)×(n +1)( p+1) block Toeplitz matrices T ρ A ( p), p ≥ 0, based on the rows of A. The connections between the ranks of the two matrices is studied by comparing the corresponding vector spaces of row relations R and R( p). A main tool are the Hankel matrices with rows in R. The dimension of R( p) is determined in terms of geometric invariants attached to the Hankel matrices with rows in R. The study of Hankel r -planes of P m , for r ≥ 1, turns out to be very useful and interesting in itself since they constitute a subvariety of the Grassmannian G(r, m).

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