About: Zeuthen–Segre invariant

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In algebraic geometry, the Zeuthen–Segre invariant I is an invariant of a projective surface found in a complex projective space which was introduced by Zeuthen and rediscovered by Corrado Segre. The invariant I is defined to be d – 4g – b if the surface has a pencil of curves, non-singular of genus g except for d curves with 1 ordinary node, and with b base points where the curves are non-singular and transverse.

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  • In algebraic geometry, the Zeuthen–Segre invariant I is an invariant of a projective surface found in a complex projective space which was introduced by Zeuthen and rediscovered by Corrado Segre. The invariant I is defined to be d – 4g – b if the surface has a pencil of curves, non-singular of genus g except for d curves with 1 ordinary node, and with b base points where the curves are non-singular and transverse. Alexander showed that the Zeuthen–Segre invariant I is χ–4, where χ is the topological Euler–Poincaré characteristic introduced by Poincaré, which is equal to the Chern number c2 of the surface. (en)
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  • Corrado Segre (en)
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  • Corrado (en)
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  • Segre (en)
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  • 1896 (xsd:integer)
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  • In algebraic geometry, the Zeuthen–Segre invariant I is an invariant of a projective surface found in a complex projective space which was introduced by Zeuthen and rediscovered by Corrado Segre. The invariant I is defined to be d – 4g – b if the surface has a pencil of curves, non-singular of genus g except for d curves with 1 ordinary node, and with b base points where the curves are non-singular and transverse. (en)
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  • Zeuthen–Segre invariant (en)
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