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Zur algebraischen Geometrie 19

In: Zur algebraischen Geometrie

Author

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  • B. L. van der Waerden

    (Universität Zürich, Mathematisches Institut)

Abstract

Zusammenfassung Es sei k ein beliebiger Konstantenkörper und V eine über k irreduzible Varietät im projektiven Raum P n . Die zugeordnete Form von V wurde von Chow und mir1) folgendermaßen definiert. Man schneide V mit r allgemeinen Hyperebenen U 1…, U r . Die Koordinaten der Hyperebenen U i sind Unbestimmte U ij (1 ≦ i ≦r, 0 ≦ j ≦ n). Wenn V nicht in der Hyperebene y 0= 0 liegt, so liegen die Schnittpunkte y ( v ) auch nicht in dieser Hyperebene, und man kann ihre Koordinaten durch y 0= 1 eindeutig normieren. Nun bildet man mit neuen Unbestimmten U 0j (j = 0,…, n) die Linearformen 1 $$ ({{U}_{0}}{{y}^{{\left( v \right)}}}) = \sum\limits_{0}^{n} {{{U}_{{0j}}}{{y}_{j}}^{{\left( v \right)}}} $$

Suggested Citation

  • B. L. van der Waerden, 1983. "Zur algebraischen Geometrie 19," Springer Books, in: Zur algebraischen Geometrie, chapter 30, pages 410-426, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-61782-9_30
    DOI: 10.1007/978-3-642-61782-9_30
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