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arXiv · 1810.10150

Stringy Hirzebruch classes of Weierstrass fibrations

James Fullwood·Mark van Hoeij
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Abstract

A Weierstrass fibration is an elliptic fibration $Y\to B$ whose total space $Y$ may be given by a global Weierstrass equation in a $\mathbb{P}^2$-bundle over $B$. In this note, we compute stringy Hirzebruch classes of singular Weierstrass fibrations associated with constructing non-Abelian gauge theories in $F$-theory. For each Weierstrass fibration $Y\to B$ we then derive a generating function $\chi^{\text{str}}_y(Y;t)$, whose degree-$d$ coefficient encodes the stringy $\chi_y$-genus of $Y\to B$ over an unspecified base of dimension $d$, solely in terms of invariants of the base. To facilitate our computations, we prove a formula for general characteristic classes of blowups along (possibly singular) complete intersections.

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James Fullwood, Mark van Hoeij. 2018-10-24. Stringy Hirzebruch classes of Weierstrass fibrations. https://arxiv.org/abs/1810.10150

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