location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword Generators

 Expand all        Collapse all Results 1 - 2 of 2

1. CJM Online first

 Minimal Generators of the Defining Ideal of the Rees Algebra Associated with a Rational Plane Parametrization with $\mu=2$ We exhibit a set of minimal generators of the defining ideal of the Rees Algebra associated with the ideal of three bivariate homogeneous polynomials parametrizing a proper rational curve in projective plane, having a minimal syzygy of degree 2. Keywords:Rees Algebras, rational plane curves, minimal generatorsCategories:13A30, 14H50
 An Algorithm for Fat Points on $\mathbf{P}^2 Let$F$be a divisor on the blow-up$X$of$\pr^2$at$r$general points$p_1, \dots, p_r$and let$L$be the total transform of a line on$\pr^2$. An approach is presented for reducing the computation of the dimension of the cokernel of the natural map$\mu_F \colon \Gamma \bigl( \CO_X(F) \bigr) \otimes \Gamma \bigl( \CO_X(L) \bigr) \to \Gamma \bigl( \CO_X(F) \otimes \CO_X(L) \bigr)$to the case that$F$is ample. As an application, a formula for the dimension of the cokernel of$\mu_F$is obtained when$r = 7$, completely solving the problem of determining the modules in minimal free resolutions of fat point subschemes\break$m_1 p_1 + \cdots + m_7 p_7 \subset \pr^2$. All results hold for an arbitrary algebraically closed ground field~$k\$. Keywords:Generators, syzygies, resolution, fat points, maximal rank, plane, Weyl groupCategories:13P10, 14C99, 13D02, 13H15