Related papers: Stringy invariants of normal surfaces

We show that in closed string topology and in open-closed string topology with one $D$-brane, higher genus stable string operations are trivial. This is a consequence of Harer's stability theorem and related stability results on the…

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 consider heterotic string solutions based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold, preserving two supercharges. The constraints on the internal manifolds with SU(3) structure are…

This article consists of two parts. The first part is a survey on the normal reduction numbers of normal surface singularities. It includes results on elliptic singularities, cone-like singularities and homogeneous hypersurface…

In this note we prove that a smooth order satisfying the reverse geometric engineering of singularities conditions in stringtheory (in any compactifying dimension) is Auslander regular. Moreover, we classify the etale local structure of…

Given a logarithmic $1$-form on the snc locus of a log canonical surface pair $(X, D)$ over a perfect field of characteristic $p \ge 7$, we show that it extends with at worst logarithmic poles to any resolution of singularities. We also…

We prove an extension of the Cheeger-M\"{u}ller theorem to spaces with isolated conical singularities: the $L^2$-analytic torsion coincides with the Ray-Singer intersection torsion on an even dimensional space, and they are trivial, while…

Let k be an uncountable field of characteristic different from two. We show that a very general hypersurface of dimension N>2 and degree at least $\log_2N +2$ is not stably rational over the algebraic closure of k.

Classical rotating closed string are folded strings. At the folding points the scalar curvature associated with the induced metric diverges. As a consequence one cannot properly quantize the fluctuations around the classical solution since…

For a generic deformation of a two-dimensional holomorphic vector field with elementary degenerate singular point (saddle-node) we express the Martinet - Ramis orbital analytic classification invariants of the nonperturbed field in terms of…

We observe that the E-resultant of a very ample rank 2 vector bundle E on a real projective curve (with no real points) is nonnegative when restricted to the space of real sections. Moreover, we show that if E has a section vanishing at…

As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these studies, they have found that inverse images of such maps…

A conjecture of Batyrev and Manin predicts the asymptotic behaviour of rational points of bounded height on smooth projective varieties over number fields. We prove some new cases of this conjecture for conic bundle surfaces equipped with…

A rational normal scroll structure on an $(n+1)$-dimensional manifold $M$ is defined as a field of rational normal scrolls of degree $n-1$ in the projectivised cotangent bundle $\mathbb{P}T^*M$. We show that geometry of this kind naturally…

We characterize all graphs whose binomial edge ideals have pure resolutions. Moreover, we introduce a new switching of graphs which does not change some algebraic invariants of graphs, and using this, we study the linear strand of the…

Let D = {D_{1},...,D_{l}} be an arrangement of smooth hypersurfaces with normal crossings on the complex projective space P^n and let \Omega^{1}_{P^n}(log D) be the logarithmic bundle attached to it. Following [1], we show that…

We introduce a new functional $\mathcal{E}_{\mathfrak{p}}$ on the space of conformal structures on an oriented projective manifold $(M,\mathfrak{p})$. The nonnegative quantity $\mathcal{E}_{\mathfrak{p}}([g])$ measures how much…

We point out that the moduli sector of the $(2,2)$ string compactification with its nonperturbatively preserved non-compact symmetries is a framework to study global topological defects. Based on the target space modular invariance of the…

In this paper we introduce some {\it variation functions} associated to the rank of the Infinitesimal Variations of Hodge Structure for a family of smooth projective complex curves. We give some bounds and inequalities and, in particular,…

We reformulate the construction of Kontsevich's completion and use Lawson homology to define many new motivic invariants. We show that the dimensions of subspaces generated by algebraic cycles of the cohomology groups of two $K$-equivalent…