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arXiv · 1112.3069

Reduced classes and curve counting on surfaces I: theory

M. Kool·R. P. Thomas
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Abstract

We develop a theory of \emph{reduced} Gromov-Witten and stable pair invariants of surfaces and their canonical bundles. We show that classical Severi degrees are special cases of these invariants. This proves a special case of the MNOP conjecture, and allows us to generalise the G\"ottsche conjecture to the non-ample case. In a sequel we prove this generalisation. We prove a remarkable property of the moduli space of stable pairs on a surface. It is the zero locus of a section of a bundle on a smooth compact ambient space, making calculation with the reduced virtual cycle possible.

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M. Kool, R. P. Thomas. 2011-12-13. Reduced classes and curve counting on surfaces I: theory. https://doi.org/10.14231/ag-2014-017

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