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Counting curves on a general linear system with up to two singular points

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arxiv 1501.01557 v1 pith:BIT5DG2D submitted 2015-01-07 math.AG math.AT

classification math.AGmath.AT
keywords numberclasscodimensioncurvesgenericpointsbundleclassical
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abstract

In this paper we obtain an explicit formula for the number of curves in a compact complex surface $X$ (passing through the right number of generic points), that has up to one node and one singularity of codimension $k$, provided the total codimension is at most $7$. We use a classical fact from differential topology: the number of zeros of a generic smooth section of a vector bundle $V$ over $M$, counted with signs, is the Euler class of $V$ evaluated on the fundamental class of $M$.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Counting curves in a linear system with upto eight singular points

    math.AG 2019-09 conditional novelty 7.0 of 10

    The authors derive recursive Euler class formulas that enumerate curves with δ nodes and one fixed singularity for all δ+k ≤ 8, recovering prior results and producing new codimension eight numbers.

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