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Computing projective equivalences of special algebraic varieties

Citace:
BIZZARRI, M., LÁVIČKA, M., VRŠEK, J. Computing projective equivalences of special algebraic varieties. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, roč. 367, č. MAR 15, s. nestránkováno. ISSN: 0377-0427
Druh: ČLÁNEK
Jazyk publikace: eng
Anglický název: Computing projective equivalences of special algebraic varieties
Rok vydání: 2020
Autoři: RNDr. Michal Bizzarri Ph.D. , doc. RNDr. Miroslav Lávička Ph.D. , RNDr. Jan Vršek Ph.D. ,
Abstrakt EN: This paper is devoted to the investigation of selected situations when computing projective (and other) equivalences of algebraic varieties can be efficiently solved via finding projective equivalences of finite sets of points on the projective line. In particular, we design a method that finds for two algebraic varieties X, Y from special classes an associated set of automorphisms of the projective line (the so called good candidate set) consisting of suitable candidates for the subsequent construction of possible mappings X -> Y. The functionality of the designed approach is presented for computing pro- jective equivalences of rational curves, determining projective equivalences of rational ruled surfaces, detecting affine transformations between planar algebraic curves, and computing similarities between two implicitly given algebraic surfaces. When possible, symmetries of given shapes are also discussed as special cases.
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