On the Minimal Resolution Conjecture for P3
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International Journal of Contemporary Mathematical Sciences
Abstract
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Int. J. Contemp. Math. Sciences, Vol. 3, 2008, no. 33, 1643 - 1655
The Minimal Resolution Conjecture that was formulated by A Lorenzini [2] has been shown to hold true for P2, P3 [3] they made use of Quadrics, here we tackle the P3 case but making use of variant methods i.e. mainly the method of Horace (m`ethode d’Horace) to evaluate sections of fibres at given points. This was introduced by A Hirschowitz in 1984 in a letter he wrote to R Hartshorne. For a general set of points P1, . . . , Pm ∈ P3, for a positive integer m, we show that the map H0P3,ΩP3 (d + 1) −→ m i=1 ΩP3 (d + 1)|Pi is of maximal rank.
The Minimal Resolution Conjecture that was formulated by A Lorenzini [2] has been shown to hold true for P2, P3 [3] they made use of Quadrics, here we tackle the P3 case but making use of variant methods i.e. mainly the method of Horace (m`ethode d’Horace) to evaluate sections of fibres at given points. This was introduced by A Hirschowitz in 1984 in a letter he wrote to R Hartshorne. For a general set of points P1, . . . , Pm ∈ P3, for a positive integer m, we show that the map H0P3,ΩP3 (d + 1) −→ m i=1 ΩP3 (d + 1)|Pi is of maximal rank.
Keywords
Maximal rank, M´ethode d’Horace