Stringy Hirzebruch classes of Weierstrass fibrations
James Fullwood, Mark van Hoeij

TL;DR
This paper computes stringy Hirzebruch classes for singular Weierstrass fibrations in F-theory, deriving generating functions for stringy $ ext{chi}_y$-genera based on base invariants.
Contribution
It introduces a method to calculate stringy Hirzebruch classes of singular Weierstrass fibrations and derives a generating function for stringy $ ext{chi}_y$-genera.
Findings
Derived a formula for characteristic classes of blowups along complete intersections.
Computed stringy Hirzebruch classes for Weierstrass fibrations.
Established a generating function for stringy $ ext{chi}_y$-genera.
Abstract
A Weierstrass fibration is an elliptic fibration whose total space may be given by a global Weierstrass equation in a -bundle over . In this note, we compute stringy Hirzebruch classes of singular Weierstrass fibrations associated with constructing non-Abelian gauge theories in -theory. For each Weierstrass fibration we then derive a generating function , whose degree- coefficient encodes the stringy -genus of over an unspecified base of dimension , 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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