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The vanishing cycles of curves in toric surfaces I

  • Rémi Crétois (a1) and Lionel Lang (a2)

This article is the first in a series of two in which we study the vanishing cycles of curves in toric surfaces. We give a list of possible obstructions to contract vanishing cycles within a given complete linear system. Using tropical means, we show that any non-separating simple closed curve is a vanishing cycle whenever none of the listed obstructions appears.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
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