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

This paper completes the classification problem which was proposed in the previous paper [1] in which we attempted to characterize the minimal models and families obtained by the tensor products and the simple current extensions of minimal models under the condition that the characters of simple modules satisfy modular differential equations of the third order, and a mild condition on vertex operator

We prove that if a smooth variety with non-positive canonical class can be embedded into a weighted projective space of dimension $n$ as a well formed complete intersection and it is not an intersection with a linear cone therein, then the weights of the weighted projective space do not exceed $n+1$. Based on this bound we classify all smooth Fano complete intersections of dimensions $4$ and $5$, and

We study the $E_1$-degeneration of the logarithmic Hodge to de Rham spectral sequence of the special fiber of a proper semistable family over a discrete valuation ring. On the one hand, we prove that the $E_1$-degeneration property is invariant under admissible blowups. Assuming functorial resolution of singularities over $\mathbb{Z}$, this implies that the $E_1$-degeneration property depends only

We show that the general Clifford double mirrors constructed in [BL18] (Lev Borisov and Zhan Li “On Clifford double mirrors of toric complete intersections”, Adv. Math., 328:300–355, 2018) are derived equivalent.

We analyze aspects of extant examples of 2d extremal chiral (super) conformal field theories with $c \leq 24$. These are theories whose only operators with dimension smaller or equal to $c/24$ are the vacuum and its (super) Virasoro descendants. The most prototypical example is the monster CFT, whose famous genus zero property is intimately tied to the Rademacher summability of its twined partition