Fat point ideals in $\mathbb{K}[\mathbb{P}^N]$ with linear minimal free resolutions and their resurgences

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Hassan Haghighi ◽  
Mohammad Mosakhani
2000 ◽  
Vol 52 (1) ◽  
pp. 123-140 ◽  
Author(s):  
Brian Harbourne

AbstractLet F be a divisor on the blow-up X of P2 at r general points p1, . . . , pr and let L be the total transform of a line on P2. An approach is presented for reducing the computation of the dimension of the cokernel of the natural map to the case that F is ample. As an application, a formula for the dimension of the cokernel of μF is obtained when r = 7, completely solving the problem of determining the modules in minimal free resolutions of fat point subschemes m1p1 + · · · + m7p7 ⊂ P2. All results hold for an arbitrary algebraically closed ground field k.


2020 ◽  
pp. 1-20
Author(s):  
Mengyuan Zhang

Abstract We study bundles on projective spaces that have vanishing lower cohomologies using their short minimal free resolutions. We partition the moduli $\mathcal{M}$ according to the Hilbert function H and classify all possible Hilbert functions H of such bundles. For each H, we describe a stratification of $\mathcal{M}_H$ by quotients of rational varieties. We show that the closed strata form a graded lattice given by the Betti numbers.


1990 ◽  
Vol 118 ◽  
pp. 203-216 ◽  
Author(s):  
Mitsuyasu Hashimoto

Let R be a Noetherian commutative ring with, unit element, and Xij be variables with 1 ≤ i ≤ m and 1 ≤ j ≤ n. Let S = R[xij] be the polynomial ring over R, and It be the ideal in S, generated by the t × t minors of the generic matrix (xij) ∈ Mm, n(S). For many years there has been considerable interest in finding a minimal free resolution of S/It, over arbitrary base ring R. If we have a minimal free resolution P. over R = Z, the ring of integers, then R′ ⊗z P. is a resolution of S/It over the base ring R′.


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