Related papers: BGG correspondence for toric complete intersection…

We review, from a didactic point of view, the definition of a toric section and the different shapes it can take. We'll then discuss some properties of this curve, investigate its analogies and differences with the most renowned conic…

We provide new logarithmic lower bounds for the torsion order of a very general complete intersection in projective space as well as a very general hypersurface in products of projective spaces and Grassmannians, in particular we prove…

Let $g_1, ..., g_k$ be tropical polynomials in $n$ variables with Newton polytopes $P_1, ..., P_k$. We study combinatorial questions on the intersection of the tropical hypersurfaces defined by $g_1, ..., g_k$, such as the $f$-vector, the…

We propose a combinatorical duality for lattice polyhedra which conjecturally gives rise to the pairs of mirror symmetric families of Calabi-Yau complete intersections in toric Fano varieties with Gorenstein singularities. Our construction…

We give an introduction to Tropical Geometry and prove some results in Tropical Intersection Theory. The first part of this paper is an introduction to tropical geometry aimed at researchers in Algebraic Geometry from the point of view of…

We describe a method of computing equivariant and ordinary intersection cohomology of certain varieties with actions of algebraic tori, in terms of structure of the zero- and one-dimensional orbits. The class of varieties to which our…

Let $G=(V,E)$ be a finite, simple graph. We consider for each oriented graph $G_{\cal O}$ associated to an orientation ${\cal O}$ of the edges of $G$, the toric ideal $P_{G_{\cal O}}$. In this paper we study those graphs with the property…

We extend our model for affine structures on toric Calabi-Yau hypersurfaces math.AG/0205321 to the case of complete intersections.

We propose a categorical version of the Boson-Fermion correspondence and its twisted version. One can view it as a relative of the Frenkel-Kac-Segal construction of quantum affine algebras.

We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these…

In this paper we give conditions on a homogeneous polynomial for which the associated graded Artin algebra is a complete intersection.

We show that the variable cohomology of a general complete intersection of quadrics can be identified with the intersection cohomology of a double covering. As a consequence, we show that the middle cohomology of a general complete…

We study normal finite abelian covers of smooth varieties. In particular we establish combinatorial conditions so that a normal finite abelian cover of a smooth variety is Gorenstein or locally complete intersection.

Let R be a commutative, noetherian, local ring. Topological Q-vector spaces modelled on full subcategories of the derived category of R are constructed in order to study intersection multiplicities.

We outline a strategy for computing intersection numbers on smooth varieties with torus actions using a residue formula of Bott. As an example, Gromov-Witten numbers of twisted cubic and elliptic quartic curves on some general complete…

This is an extended example of the study of mirror symmetry via log schemes and the discrete Legendre transform on affine manifolds, introduced by myself and Bernd Siebert in "Mirror Symmetry via Logarithmic Degeneration Data I"…

We study obstructions to existence of non-commutative crepant resolutions, in the sense of Van den Bergh, over local complete intersections.

We give a proof of the $p$-adic weight monodromy conjecture for scheme-theoretic complete intersections in projective smooth toric varieties. The strategy is based on Scholze's proof in the $\ell$-adic setting, which we adapt using…

The height of a toric variety and that of its hypersurfaces can be expressed in convex-analytic terms as an adelic sum of mixed integrals of their roof functions and duals of their Ronkin functions. Here we extend these results to the…

In this paper we calculate the elliptic genus of certain complete intersections in products of projective spaces. We show that it is equal to the elliptic genus of the Landau-Ginzburg models that are, according to Hori and Vafa, mirror…