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The enumerative geometry of plane cubics. I. Smooth cubics


Author: Paolo Aluffi
Journal: Trans. Amer. Math. Soc. 317 (1990), 501-539
MSC: Primary 14N10; Secondary 14C17
DOI: https://doi.org/10.1090/S0002-9947-1990-0972700-4
MathSciNet review: 972700
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct a variety of complete plane cubics by a sequence of five blow-ups over $ {\mathbb{P}^9}$. This enables us to translate the problem of computing characteristic numbers for a family of plane cubics into one of computing five Segre classes, and to recover classic enumerative results of Zeuthen and Maillard.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1990-0972700-4
Keywords: Complete conics, complete cubics, blow-up, Segre class
Article copyright: © Copyright 1990 American Mathematical Society

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