Curves in Calabi-Yau threefolds and topological quantum field theory

DOI10.1215/S0012-7094-04-12626-0zbMATH Open1084.14053arXivmath/0306316OpenAlexW2068060755MaRDI QIDQ1769583

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Publication date: 4 April 2005

Published in: (Search for Journal in Brave)

Abstract: We continue our study of the local Gromov-Witten invariants of curves in Calabi-Yau 3-folds. We define relative invariants for the local theory which give rise to a 1+1-dimensional TQFT taking values in the ring Qt. The associated Frobenius algebra over Qt is semisimple. Consequently, we obtain a structure result for the local invariants. As an easy consequence of our structure formula, we recover the closed formulas for the local invariants in case either the target genus or the degree equals 1.

Full work available at URL: https://arxiv.org/abs/math/0306316

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