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Numbers for reducible cubic scrolls.

Israel Vainsencher1, Fernando Xavier

  • 1ICEX, Departamento de Matemática, UFMG, Cx. Postal 702 Belo Horizonte, 30123-970 Belo Horizonte, MG, Brazil. israel@mat.ufmg.br

Anais Da Academia Brasileira De Ciencias
|November 24, 2004
PubMed
Summary

This study presents a method for calculating the quantity of reducible cubic scrolls with codimension 2 in projective spaces (Pn). The research focuses on scrolls connected to a specific number of linear spaces.

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Area of Science:

  • Algebraic Geometry
  • Enumerative Geometry

Background:

  • Cubic scrolls are fundamental objects in algebraic geometry.
  • Understanding their properties and counts is crucial for classifying geometric structures.

Purpose of the Study:

  • To develop a computational method for determining the number of reducible cubic scrolls.
  • To analyze scrolls of codimension 2 in projective spaces (Pn).

Main Methods:

  • Utilizing techniques from enumerative geometry.
  • Applying intersection theory to count geometric objects.

Main Results:

  • A formula is derived for the number of reducible cubic scrolls of codimension 2 in Pn.
  • The computation is shown to be dependent on the number of incident linear spaces.

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Conclusions:

  • The study provides a concrete method for enumerating specific algebraic varieties.
  • This work contributes to the understanding of geometric counting problems in higher dimensions.