First steps with Bott formula

Mustapha Lahyane, Israel Moreno-Mejía, Dan Silva-López

Abstract


We use Bott's residue formula to infer that a general cubic surface in the projective space ℙ3ℂ contains exactly twenty seven lines and that a general complete intersection of two quadrics in ℙ4ℂ contains exactly sixteen lines.

Keywords


Bott’s residue formula, complete intersection, torus action, rational surfaces.

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DOI: https://doi.org/10.1478/AAPP.1012LC1

Copyright (c) 2023 Mustapha Lahyane, Israel Moreno-Mejía, Dan Silva-López

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