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Schemata I

In: Kommutative Algebra und Algebraische Geometrie

Author

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  • Jürgen Böhm

Abstract

Zusammenfassung Schemata sind lokal geringte Räume, lokal isomorph zu affinen Schemata. Es folgen grundlegende topologische Tatsachen über Schemata, Konstruktion von Faserprodukten, offene und abgeschlossene Unterschemata, wichtige Klassen von Morphismen (Immersionen, endliche, affine Morphismen und Morphismen vom endlichen Typ, quasikompakte, separierte und eigentliche Morphismen). Weitere Stichworte sind: bewertungstheoretische Kriterien für Separiertheit und Eigentlichkeit, (quasi-)kohärente Modulgarben, schematheoretisches Bild, konstruierbare Mengen, projektive Limites von Schemata, Dimensionstheorie, Varietäten, allgemeiner Satz von Bezout, projektive Schemata, Endlichkeitssatz für kohärente Garben über projektiven Schemata, projektive Morphismen, Veronese- und Segre-Abbildung, ample und sehr ample Linienbündel,Weil-Divisoren, Cartier-Divisoren, projektive Bündel über Algebrengarben und Aufblasungen, Kähler-Differentiale, reguläre Untervarietäten, vollständige Durchschnitte, Bertini-Theorem.

Suggested Citation

  • Jürgen Böhm, 2019. "Schemata I," Springer Books, in: Kommutative Algebra und Algebraische Geometrie, chapter 0, pages 263-403, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-59482-7_5
    DOI: 10.1007/978-3-662-59482-7_5
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