@inbook{db03fe3f06464ab1b70ecbb38f81cbfc,

title = "On the motivic stable pairs invariants of K3 surfaces",

abstract = "For a K3 surface S and a class β ∈ Pic(S), we study motivic invariants of stable pairs moduli spaces associated to 3-fold thickenings of S. We conjecture suitable deformation and divisibility invariances for the Betti realization. Our conjectures, together with earlier calculations of Kawai-Yoshioka, imply a full determination of the theory in terms of the Hodge numbers of the Hilbert schemes of points of S. The work may be viewed as the third in a sequence of formulas starting with Yau-Zaslow and Katz-Klemm-Vafa (each recovering the former). Numerical data suggest the motivic invariants are linked to the Mathieu M24 moonshine phenomena. The KKV formula and the Pairs/Noether-Lefschetz correspondence together determine the BPS counts of K3-fibered Calabi-Yau 3-folds in fiber classes in terms of modular forms. We propose a framework for a refined P/NL correspondence for the motivic invariants of K3-fibered CY 3-folds. For the STU model, a complete conjecture is presented.",

author = "S. Katz and A. Klemm and R. Pandharipande and Thomas, {R. P.}",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.",

year = "2016",

doi = "10.1007/978-3-319-29959-4_6",

language = "English (US)",

series = "Progress in Mathematics",

publisher = "Springer Basel",

pages = "111--146",

booktitle = "Progress in Mathematics",

}