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Displaying similar documents to “BPS states of curves in Calabi-Yau 3-folds.”

Comparison theorems for Gromov–Witten invariants of smooth pairs and of degenerations

Dan Abramovich, Steffen Marcus, Jonathan Wise (2014)

Annales de l’institut Fourier

Similarity:

We consider four approaches to relative Gromov–Witten theory and Gromov–Witten theory of degenerations: J. Li’s original approach, B. Kim’s logarithmic expansions, Abramovich–Fantechi’s orbifold expansions, and a logarithmic theory without expansions due to Gross–Siebert and Abramovich–Chen. We exhibit morphisms relating these moduli spaces and prove that their virtual fundamental classes are compatible by pushforward through these morphisms. This implies that the Gromov–Witten invariants...

Finite type invariants for cyclic equivalence classes of nanophrases

Yuka Kotorii (2014)

Fundamenta Mathematicae

Similarity:

We define finite type invariants for cyclic equivalence classes of nanophrases and construct universal invariants. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is known that extended Arnold basic invariants to signed words are finite type invariants of degree 2, by Fujiwara's work. We give another proof of this result and show that those invariants do not provide the universal one of degree 2.