Related papers: On the PSL(2,19)-invariant cubic sevenfold

The ring of projective invariants of eight ordered points on the line is a quotient of the polynomial ring on V, where V is a fourteen-dimensional representation of S_8, by an ideal I_8, so the modular fivefold (P^1)^8 // GL(2) is Proj(Sym*…

In mathematical physics the Galois top, introduced by S. Adlaj, possesses a fixed point on one of two Galois axes through its center of mass. This heavy top has two algebraic motion invariants and an additional transcendental…

We prove a flat torus theorem for quadric complexes. In particular, we show that if a non-cyclic free abelian group $G$ acts metrically properly on a quadric complex $X$, then $G \cong \mathbb{Z}^2$ and $X$ contains a $G$-invariant…

Consider the algebraic dynamics on a torus T=G_m^n given by a matrix M in GL_n(Z). Assume that the characteristic polynomial of M is prime to all polynomials X^m-1. We show that any finite equivariant map from another algebraic dynamics…

The theory of coverings of the two-dimensional torus is a standard part of algebraic topology and has applications in several topics in string theory, for example, in topological strings. This paper initiates applications of this theory to…

We consider a real Abelian Lie supergroup $G$ acting on its complexification $M$, equipped with a $G$-invariant super K\"ahler form. We extend the scheme of classical geometric quantization to this setting and construct a unitary…

We propose a generalization of the topological vertex, which we call the "non-commutative topological vertex". This gives open BPS invariants for a toric Calabi-Yau manifold without compact 4-cycles, where we have D0/D2/D6-branes wrapping…

For a general cubic fourfold, it was observed by Donagi and Markman that the relative intermediate Jacobian fibration associated to the family of its hyperplane sections carries a natural holomorphic symplectic form making the fibration…

The abelian sandpile models feature a finite abelian group G generated by the operators corresponding to particle addition at various sites. We study the canonical decomposition of G as a product of cyclic groups G = Z_{d_1} X Z_{d_2} X…

Let L --> X be a complex line bundle over a compact connected Riemann surface. We consider the abelian vortex equations on L when the metric on the surface has finitely many point degeneracies or conical singularities and the line bundle…

We study linearizability of actions of finite groups on singular cubic threefolds, using cohomological tools, intermediate Jacobians, Burnside invariants, and the equivariant Minimal Model Program.

We study the behaviour on some nodal hyperplanes of the isomorphism, described in a paper of 2019 by Boissi\`ere, Camere and Sarti, between the moduli space of smooth cubic threefolds and the moduli space of hyperk\"ahler fourfolds of…

We present a computational method for detecting highly singular members in families of algebraic varieties. Applying this approach to a family of numerical Godeaux surfaces, we obtain explicit examples with many singularities. In…

We define and study a biadditive symmetric (not necessarily perfect) pairing on the torsion part $\mathrm{Pic}(X)_{\mathrm{tors}}$ of the Picard group of a smooth projective curve $X$ over a field $k$ with values in $k^\times \otimes…

We study smooth cubic fourfolds admitting an automorphism of order $7$. It is known that the possible symplectic automorphism groups of such cubic fourfolds are precisely $F_{21}$, $\mathrm{PSL}(2,\mathbb{F}_7)$, and $A_7$. In this paper,…

We prove a special case of a conjecture of Davison which pertains to superpotential descriptions of fundamental group algebras $k[\pi_1(X)]$. We consider the case in which the manifold $X$ is the mapping torus $M_{g, \varphi}$ of a genus…

We obtain, by a direct computation, explicit descriptions of all principally polarized semi-abelic varieties of torus rank up to 3. We describe the geometry of their symmetric theta divisors and obtain explicit formulas for the involution…

Let $SU_X(n,L)$ be the moduli space of rank n semistable vector bundles with fixed determinant L on a smooth projective genus g curve X. Let $SU_X^s(n,L)$ denote the open subset parametrizing stable bundles. We show that if g>3 and n > 1,…

Let G be a group of automorphisms of a compact K\"ahler manifold X of dimension n and N(G) the subset of null-entropy elements. Suppose G admits no non-abelian free subgroup. Improving the known Tits alternative, we obtain that, up to…

Let $A$ be an abelian surface over $\mathbb{Q}$ whose geometric endomorphism ring is a maximal order in a non-split quaternion algebra. Inspired by Mazur's theorem for elliptic curves, we show that the torsion subgroup of $A(\mathbb{Q})$ is…