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Computing subschemes of the border basis scheme. (English) Zbl 07276757
13C40 Linkage, complete intersections and determinantal ideals
14M10 Complete intersections
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13P99 Computational aspects and applications of commutative rings
14Q99 Computational aspects in algebraic geometry
Full Text: DOI
[1] J. Abbott, A. M. Bigatti and L. Robbiano, CoCoA: A system for doing computations in commutative algebra, available at http://cocoa.dima.unige.it.
[2] Bertone, C., Cioffi, F. and Roggero, M., Smoothable Gorenstein points via marked schemes and double-generic initial ideals, Exp. Math. (2019), https://doi.org/10.1080/10586458.2019.1592034.
[3] Casnati, G., Jelisiejew, J. and Notari, R., Irreducibility of the Gorenstein loci of Hilbert schemes via ray families, Algebra Number Theory9 (2015) 1525-1570. · Zbl 1349.14011
[4] Casnati, G. and Notari, R., On the Gorenstein locus of some punctual Hilbert schemes, J. Pure Appl. Algebra213 (2009) 2055-2074. · Zbl 1169.14003
[5] Casnati, G. and Notari, R., On the irreducibility and the singularities of the Gorenstein locus of the punctual Hilbert scheme of degree 10, J. Pure Appl. Algebra215 (2011) 1243-1254. · Zbl 1215.14009
[6] V. Drinfeld, On algebraic spaces with an action of \(G_m\), preprint (2013), arXiv:math 1308.2604 [math.AG].
[7] Eisenbud, D., Commutative Algebra with a View Toward Algebraic Geometry, , Vol. 150 (Springer-Verlag, New York, 1995). · Zbl 0819.13001
[8] Grothendieck, A., Techniques de construction et théorèmes d’existence en géométrie algébrique IV: les schémas de Hilbert, Asterisque6 (1960-1961) 249-276.
[9] Haiman, M., \(t, q\)-Catalan numbers and the Hilbert scheme, Discrete Math.193 (1998) 201-224. · Zbl 1061.05509
[10] M. Huibregtse, The cotangent space at a monomial ideal of the Hilbert scheme of points of an affine space, preprint (2005), arXiv:math/0506.575[math.AG].
[11] Huibregtse, M., An elementary construction of the multigraded Hilbert scheme of points, Pac. J. Math.223 (2006) 269-315. · Zbl 1113.14007
[12] Iarrobiano, A. and Kanev, V., Power Sums, Gorenstein Algebras and Determinantal Loci, , Vol. 1721 (Springer-Verlag, Berlin, 1999).
[13] Jelisiejew, J. and Sienkiewicz, Ł., Białynicki-Birula decomposition for reductive groups, J. Math. Pures Appl.131 (2019) 290-325. · Zbl 1446.14030
[14] Kreuzer, M., Long, L. N. and Robbiano, L., On the Cayley-Bacharach property, Commun. Algebra47 (2019) 328-354. · Zbl 1419.13046
[15] M. Kreuzer, L. N. Long and L. Robbiano, Algorithms for checking zero-dimensional complete intersections, preprint (2019), arXiv:math/1903.09563 [math.AG].
[16] M. Kreuzer, L. N. Long and L. Robbiano, Computing subschemes of the border basis scheme (2017-2019), https://www.symbcomp.fim.uni-passau.de/en/projects/.
[17] Kreuzer, M. and Robbiano, L., Computational Commutative Algebra 1 (Springer, Heidelberg, 2000). · Zbl 0956.13008
[18] Kreuzer, M. and Robbiano, L., Computational Commutative Algebra 2 (Springer, Heidelberg, 2005). · Zbl 1090.13021
[19] Kreuzer, M. and Robbiano, L., Deformations of border bases, Collect. Math.59 (2008) 275-297. · Zbl 1190.13022
[20] Kreuzer, M. and Robbiano, L., The geometry of border bases, J. Pure Appl. Algebra215 (2011) 2005-2018. · Zbl 1216.13018
[21] Kreuzer, M. and Robbiano, L., Computational Linear and Commutative Algebra (Springer, Heidelberg, 2016). · Zbl 1360.13001
[22] Robbiano, L., On border basis and Gröbner basis schemes, Collect. Math.60 (2009) 11-25. · Zbl 1176.13004
[23] B. Sipal, Border basis schemes, dissertation, University of Passau, Passau (2017).
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