Related papers: Characteristic numbers of crepant resolutions of W…

To every elliptic Calabi-Yau threefold with a section $X$ there can be associated a Lie group $G$ and a representation $\rho$ of that group. The group is determined from the Weierstrass model, which has singularities that are generically…

A genus one curve of degree 5 is defined by the 4 x 4 Pfaffians of a 5 x 5 alternating matrix of linear forms on P^4. We describe a general method for investigating the invariant theory of such models. We use it to explain how we found our…

We provide an explicit desingularization and study the resulting fiber geometry of elliptically fibered fourfolds defined by Weierstrass models admitting a split A_4 singularity over a divisor of the discriminant locus. Such varieties are…

We construct Euler and Stiefel-Whitney classes of vector bundles with quadratic form by analyzing the intersection theory of the associated quadric bundles. We also compute the Chow rings of quadric and isotropic flag bundles. Along the…

We study modular fibers of elliptic differentials, which are roughly spaces of torus-coverings over a fixed base torus. For genus 2 torus covers with fixed degree we show, that the modular fibers F_d(1,1) are itself connected torus covers…

A theorem of Batyrev's asserts that if two nonsingular varieties V,W are birational, and their canonical bundles agree after pull-back to a resolution of indeterminacies of a birational map between them, then the Betti numbers of V and W…

Let G be a finite, complex reflection group and f its discriminant polynomial. The fibers of f admit commuting actions of G and a cyclic group. The virtual $G\times C_m$ character given by the Euler characteristic of the fiber is a…

For an $n$-fold geometrically cyclic branched covering $Y$ of a smooth, projective scheme $X$ branched at a smooth closed subscheme $Z\subset X$ with $n \in k^\times$, we compute the quadratic Euler characteristic of $Y$ in terms of certain…

Let $f: W \rightarrow T$ be an elliptic threefold that is a Weierstrass model, which is locally defined by $y^2 = x^3 + fx + g$ over $T$, with a singular fiber such that $(f,g,4f^3 + 27g^2)$ vanishes of order $(4,6,12)$ over an isolated…

The aim of this note is to use elementary methods to give a large class of examples of projective varieties $ Y \subseteq \mathbb{P}^d_k$ over a field $k$ with the property that $Y$ is not isomorphic to a hypersurface $H\subseteq…

Global F-theory compactifications whose fibers are realized as complete intersections form a richer set of models than just hypersurfaces. The detailed study of the physics associated with such geometries depends crucially on being able to…

We study F-theory duals of singular heterotic K3 models that correspond to abelian toroidal orbifolds $T^4/Z_N$. While our focus is on the standard embedding, we also comment on models with Wilson lines and more general gauge embeddings. In…

We study the geometry of elliptic fibrations satisfying the conditions of Step 8 of Tate's algorithm. We call such geometries F$_4$-models, as the dual graph of their special fiber is the twisted affine Dynkin diagram…

This paper shows that the integral equivariant cohomology Chern numbers completely determine the equivariant geometric unitary bordism classes of closed unitary $G$-manifolds, which gives an affirmative answer to the conjecture posed by…

We consider 18 families of elliptic Calabi--Yaus which arise in constructing $F$-theory compactifications of string vacua, and show in each case that the upper Hodge diamond of a crepant resolution of the associated Weierstrass model…

We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family $\GR \to B$ of Lie groups (these families are called ``gauge-invariant families'' in what follows). If the fibers…

The purpose of this paper is to construct a crepant resolution of quotient singularities by trihedral groups ( finite subgroups of SL(3,C) of certain type ), and prove that each Euler number of the minimal model is equal to the number of…

This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. --- and their associated…

A cocycle $\Omega: P \times G \to H$ taking values in a Lie group $H$ for a free right action of $G$ on $P$ defines a principal bundle $Q$ with the structure group $H$ over $P/G.$ The Chern character of a vector bundle associated to $Q$…

We study $\mathbb{S}_n$-equivariant weight-graded and topological Euler characteristics of the universal Picard stack $\mathrm{Pic}_{g, n}^d \to \mathcal{M}_{g, n}$ of degree-$d$ line bundles over $\mathcal{M}_{g, n}$. We prove that in the…