Related papers: On Cannon cone types and vector-valued multiplicat…

We prove equality of the vector field (iterated commutator) type and the regular contact type, which together with the Bloom theorem on equality of the Levi-form type and the regular contact type provides a complete solution of a long…

A vector species is a functor from the category of finite sets with bijections to vector spaces; informally, one can view this as a sequence of $S_n$-modules. A Hopf monoid (in the category of vector species) consists of a vector species…

This note describes minimal surfaces $S$ of general type satisfying $p_g\geq 5$ and $K^2=2p_g$. For $p_g\geq 8$ the canonical map of such surfaces is generically finite of degree 2 and the bulk of the paper is a complete characterization of…

We construct finite $R$-matrices for the first fundamental representation $V$ of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ for classical $\mathfrak{g}$, both through the decomposition of $V\otimes V$ into irreducibles…

The goal of this paper is to explicitly detect all the arithmetic genera of arithmetically Cohen-Macaulay projective curves with a given degree $d$. It is well-known that the arithmetic genus $g$ of a curve $C$ can be easily deduced from…

We use Macaulay2 for several enriched counts in GW(k). First, we compute the count of lines on a general cubic surface using Macaulay2 over Fp in GW(Fp) for p a prime number and over the rational numbers Q in GW(Q). This gives a new proof…

We compute Gromov-Witten invariants of any genus for del Pezzo surfaces of degree $\ge2$. The genus zero invariants have been computed a long ago, Gromov-Witten invariants of any genus for del Pezzo surfaces of degree $\ge3$ have been found…

We classify minimal complex surfaces of general type with $p_g=q=3$. More precisely, we show that such a surface is either the symmetric product of a curve of genus 3 or a free $\Z_2-$quotient of the product of a curve of genus 2 and a…

We consider recognizable evaluations for a suitable category of oriented two-dimensional cobordisms with corners between finite unions of intervals. We call such cobordisms thin flat surfaces. An evaluation is given by a power series in two…

This article reports on an approach to point counting on algebraic varieties over finite fields that is based on a detailed investigation of the $2$-adic orthogonal group. Combining the new approach with a $p$-adic method, we count the…

We study optimal simple second-order cone representations (a particular subclass of second-order cone representations) for weighted geometric means, which turns out to be closely related to minimum mediated sets. Several lower and upper…

In this paper we introduce a formula to compute Chern classes of fibered products of algebraic surfaces. For f, a generic projection to CP^2, of an algebraic surface X, we define X_k (for k smaller than degf) to be the k products of X over…

We describe an algorithm to compute the number of points over finite fields on a broad class of modular curves: we consider quotients $X_H/W$ for $H$ a subgroup of $\GL_2(\mathbb Z/n\mathbb Z)$ such that for each prime $p$ dividing $n$, the…

Zagier observed that modular Nahm sums associated with the same matrix may form a vector-valued modular function on some congruence subgroup. We establish modular transformation formulas for several families of Nahm sums by viewing them as…

We give an algorithm that, for a given value of the geometric genus $p_g,$ computes all regular product-quotient surfaces with abelian group that have at most canonical singularities and have canonical system with at most isolated base…

We continue our computation, using a combinatorial method based on Gronthendieck's dessins d'enfant, of the number of (weak) equivalence classes of surface branched covers matching certain specific branch data. In this note we concentrate…

Finite dimensional simple modules of quantum affine algebras of type A correspond to semistandard Young tableaux of rectangular shapes. In this paper, we classify all prime modules corresponding to 2-column semistandard Young tableaux, up…

We prove that the maximal number of conics, a priori irreducible of reducible, on a smooth spatial quartic surface is 800, realized by a unique quartic. We also classify quartics with many (at least 720) conics. The maximal number of real…

A basic combinatorial invariant of a convex polytope $P$ is its $f$-vector $f(P)=(f_0,f_1,\dots,f_{\dim P-1})$, where $f_i$ is the number of $i$-dimensional faces of $P$. Steinitz characterized all possible $f$-vectors of $3$-polytopes and…

We show that the number of numerical semigroups with multiplicity three, four or five and fixed genus is increasing as a function in the genus. To this end we use the Kunz polytope for these multiplicities. Counting numerical semigroups…