caa a22 4500 475741706 CHVBK 20180406123501.0 cr unu---uuuuu 170329e20000301xx s 000 0 eng 10.1007/BF02676671 doi (NATIONALLICENCE)springer-10.1007/BF02676671 Tikhomirov S. K. D. Ushinskii Yaroslavl State Pedagogical University, USSR aut Punctual hilbert schemes of small length in dimensions 2 and 3 [Elektronische Daten] [S. Tikhomirov] The biregular geometry of punctual Hilbert schemes in dimensions 2 and 3, i.e., of schemes parametrizing fixed-length zero-dimensional subschemes supported at a given point on a smooth surface or a smooth three-dimensional variety, is studied. A precise biregular description of these schemes has only been known for the trivial cases of lengths 3 and 4 in dimension 2. The next case of length 5 in dimension 2 and the two first nontrivial cases of lengths 3 and 4 in dimension 3 are considered. A detailed description of the biregular properties of punctual Hilbert schemes and of their natural designularizations by varieties of complete punctual flags is given. Kluwer Academic/Plenum Publishers, 2000 punctual Hilbert scheme nationallicence complete punctual flag nationallicence biregular description nationallicence desingularization nationallicence Ext-groups nationallicence Stein expansion nationallicence Briançon classification nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/3(2000-03-01), 348-364 0001-4346 67:3<348 2000 67 11006 https://doi.org/10.1007/BF02676671 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02676671 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Tikhomirov S. K. D. Ushinskii Yaroslavl State Pedagogical University, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/3(2000-03-01), 348-364 0001-4346 67:3<348 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer