相关论文: Motives of melonic graphs

We study the exactness of certain combinatorially defined complexes which generalize the Orlik-Solomon algebra of a geometric lattice. The main results pertain to complex reflection arrangements and their restrictions. In particular, we…

We introduce the notion of a polyptych lattice, which encodes a collection of lattices related by piecewise linear bijections. We initiate a study of the new theory of convex geometry and polytopes associated to polyptych lattices. In…

We provide a new perspective on the divisor theory of graphs, using additive combinatorics. As a test case for this perspective, we compute the gonality of certain families of outerplanar graphs, specifically the strip graphs. The Jacobians…

We study the behavior of the Chern classes of graph hypersurfaces under the operation of deletion-contraction of an edge of the corresponding graph. We obtain an explicit formula when the edge satisfies two technical conditions, and prove…

We consider the algebra M_k(C) of k-by-k matrices over the complex numbers and view it as a crossed product with a group G of order k by embedding G in the symmetric group S_k via the regular representation and embedding S_k in M_k(C) in…

The Grothendieck monoid of an exact category is a monoid version of the Grothendieck group. We use it to classify Serre subcategories of an exact category and to reconstruct the topology of a noetherian scheme. We first construct bijections…

Standard combinatorial construction, due to Kontsevich, associates to any $\ai$-algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We propose an…

In two seminal papers Kontsevich used a construction called_graph homology_ as a bridge between certain infinite dimensional Lie algebras and various topological objects, including moduli spaces of curves, the group of outer automorphisms…

The conjugation action of the complex orthogonal group on the polynomial functions on $n \times n$ matrices gives rise to a graded algebra of invariant polynomials. A spanning set of this algebra is in bijective correspondence to a set of…

This paper is based on a series of talks given at the Patejdlovka Enumeration Workshop held in the Czech Republic in November 2007. The topics covered are as follows. The graph polynomial, Tutte-Grothendieck invariants, an overview of…

We define a theory of etale motives over a noetherian scheme. This provides a system of categories of complexes of motivic sheaves with integral coefficients which is closed under the six operations of Grothendieck. The rational part of…

We provide a stratification of the $\mathrm{AGL}_r(\mathbb{C})$-representation variety of the fundamental group of the complement of a twisted Hopf link in terms of a stratification of the corresponding…

We show that the Grothendieck period conjecture holds for the Kummer surface associated with the square of a CM elliptic curve. This means that the period isomorphism is dense in the torsor of motivic periods. In other words, the…

We give necessary conditions for a category fibred in pseudo-abelian additive categories over the classifying topos of a profinite group to be a stack; these conditions are sufficient when the coefficients are $\mathbf{Q}$-linear. This…

We study tautological classes on the moduli space of stable $n$-pointed hyperelliptic curves of genus $g$ with rational tails. Our result gives a complete description of tautological relations. The method is based on the approach of Yin in…

We define for every affine Coxeter graph a certain factor group of the associated Artin group and prove that some of these groups appear as orbifold fundamental groups of moduli spaces. Examples are the moduli space of nonsingular cubic…

We study classes $P_{g,T}(\alpha;\beta)$ on the moduli space of stable, genus g curves with rational tails defined by pushing forward the virtual fundamental classes of spaces of relative stable maps to an unparameterized projective line. A…

It is proved in this paper that a locally complete intersection curve in a smooth affine C-algebra with trival conormal bundle is a set theoretic complete intersection if its corresponding class in the Grothendieck Group is torsion.

We prove a formula for the multidegrees of a rational map defined by generalized monomials on a projective variety, in terms of integrals over an associated Newton region. This formula leads to an expression of the multidegrees as volumes…

We construct symmetric monoidal categories $\LRF, \FD$ of rooted forests and Feynman graphs. These categories closely resemble finitary abelian categories, and in particular, the notion of Ringel-Hall algebra applies. The Ringel-Hall Hopf…