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One way of counting geometric objects is to construct a virtual cycle of the moduli space parametrising those objects. Then a virtual counting is obtained by an integration over the cycle. In this manuscript, we review the construction of virtual cycles of Li-Tian [LT] and Behrend-Fantechi [BF]. Then we introduce various useful methods for their study.

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An Introduction to Virtual Cycles—Via Classical Algebraic Geometry

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  • 发表日期：

    2025年

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  • Jeongseok Oh

摘要

One way of counting geometric objects is to construct a virtual cycle of the moduli space parametrising those objects. Then a virtual counting is obtained by an integration over the cycle. In this manuscript, we review the construction of virtual cycles of Li-Tian [LT] and Behrend-Fantechi [BF]. Then we introduce various useful methods for their study.