Related papers: Stringy Hodge numbers of strictly canonical nondeg…
Consider a polynomial $f$ with a convenient Newton polytope $P$ and generic complex coefficients. By the global version of the Kouchnirenko formula, the hypersurface $\{f = 0\} \subset \mathbb{C}^n$ has the homotopy type of a bouquet of…
We show that every $\mu$-constant family of isolated hypersurface singularities satisfying a nondegeneracy condition in the sense of Kouchnirenko, is topologically trivial, also is equimultiple.
Based on some analogies with the Hodge theory of isolated hypersurface singularities, we define Hodge-type numerical invariants (called H-numbers) of any, not necessarily algebraic, link in $S^3$. They contain the same information as the…
Using Newton polyhedra and non-degeneracy of matrices we present conditions which guarantee the Whitney equisingularity of families of isolated determinantal singularities.
Low-energy effective field theories arising from Calabi-Yau string compactifications are generically inconsistent or ill-defined at the classical level because of conifold singularities in the moduli space. It is shown, given a plausible…
We consider the Ehrhart polynomial of hypersimplices. It is proved that these polynomials have positive coefficients and we give a combinatorial formula for each of them. This settles a problem posed by Stanley and also proves that uniform…
Multiply-connected Calabi-Yau threefolds are of particular interest for both string theorists and mathematicians. Recently it was pointed out that one of the generic degenerations of these spaces (occurring at codimension one in moduli…
We perform the first systematic analysis of particle spectra obtained from heterotic string compactifications on non-Abelian toroidal orbifolds. After developing a new technique to compute the particle spectrum in the case of standard…
We use Batyrev-Borisov's formula for the generating function of stringy Hodge numbers of Calabi-Yau varieties realized as complete intersections in toric varieties in order to get closed form expressions for Hodge numbers of Calabi-Yau…
We prove formulae for the Hodge numbers of big resolutions of singular hypersurfaces satisfying a Bott-type vanishing condition.
We show that minimal models of nondegenerated hypersufaces defined by Laurent polynomials with a $d$-dimensional Newton polytope $\Delta$ are Calabi-Yau varieties $X$ if and only if the Fine interior of $\Delta$ consists of a single lattice…
We make use of an internal symmetry of a truncation of the bosonic sector of the superstring and N=4 supergravity theories to write down an analogue of Robinson's identity for the black holes of this theory. This allows us to prove the…
Let $X$ be an arbitrary smooth $n$-dimensional projective variety. It was discovered by Libgober and Wood that the product of the Chern classes $c_1(X)c_{n-1}(X)$ depends only on the Hodge numbers of $X$. This result has been used by…
This article describes a normal form algorithm for the Brieskorn lattice of an isolated hypersurface singularity. It is the basis of efficient algorithms to compute the Bernstein-Sato polynomial, the complex monodromy, and Hodge-theoretic…
We prove that hypersurfaces defined by irreducible square-free polynomials have rational singularities. As an easy consequence, we deduce that certain (possibly non-square-free) polynomials associated to pairs of square-free polynomials…
When $k<n$, we study the coherent systems that come from a BGN extension in which the quotient bundle is strictly semistable. In this case we describe a stratification of the moduli space of coherent systems. We also describe the strata as…
We study the first-order $\alpha'$ corrections to the singular 4-dimensional massless stringy black holes studied in the nineties in the context of the Heterotic Superstring. We show that the $\alpha'$ corrections not only induce a…
We study the weighted spectrum and vanishing cohomology for several classes of isolated hypersurface singularities, and how they contribute to the limiting mixed Hodge structure of a smoothing. Applications are given to several types of…
We provide a new, geometric proof of the motivic monodromy conjecture for non-degenerate hypersurfaces in dimension $3$, which has been proven previously by the work of Lemahieu--Van Proeyen and Bories--Veys. More generally, given a…
We study exclusive scattering of `hadrons' at high energy and fixed angle in (nonconformal) noncommutative gauge theories. Via gauge-string duality, we show that the noncommutativity renders the scattering soft, leading to exponential…