Related papers: Algebraic Gromov ellipticity: a brief survey
We give a characterization of all complete smooth toric varieties whose rational homotopy is of elliptic type. All such toric varieties of complex dimension not more than three are explicitly described.
Two Lie algebraic forms of the 2-body Elliptic Calogero model are presented. Translation-invariant and dilatation-invariant discretizations of the model are obtained.
We survey recent developments in the study of Hodge theoretic aspects of Alexander-type invariants associated with smooth complex algebraic varieties.
We construct Gromov-Witten invariants of general symplectic manifolds.
This survey paper concerns elliptic surfaces with section. We give a detailed overview of the theory including many examples. Emphasis is placed on rational elliptic surfaces and elliptic K3 surfaces. To this end, we particularly review the…
We classify the possible torsion structures of rational elliptic curves over sextic number fields.
We will pursue a way of building up an algebraic structure that involves, in a mathematical abstract way, the well known Grassmann variables. The problem arises when we tried to understand the grassmannian polynomial expansion on the scope…
This is a survey on coarse geometry with an emphasis on coarse homology theories.
This is a brief survey on the current state of play on the programs to classify infinite dimensional Hopf algebras of Gel'fand-Kirillov dimension one or two. We list a number of open questions and suggest directions for future work.
Let $X$ be a smooth complex projective algebraic variety. Let $\mathcal{G}$ be a $G$-banded gerbe with $G$ a finite abelian group. We prove an exact formula expressing genus $g$ orbifold Gromov-Witten invariants of $\mathcal{G}$ in terms of…
This article presents a comprehensive overview and supplement to recent developments in second-order elliptic partial differential equations formulated in double divergence form, along with an exploration of their parabolic counterparts.
We study the elliptic modular surface attached to the commutator subgroup of the modular group. This has an elliptic curve as base and only one singular fibre. We employ an algebraic approach and then consider some arithmetic questions.
It is proved that the rank of an elliptic curve is one less the arithmetic complexity of the corresponding non-commutative torus. As an illustration, we consider a family of elliptic curves with complex multiplication.
We study monodromy groups of elliptic fibrations over the projective line.
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
In This paper, we survey recent progress on the theory of Gromov- Witten invariants on Hilbert schemes of points mainly on elliptic surfaces and simply connected minimal surface of general type. In particular, we focus on the aspects of…
We recursively compute the Gromov-Witten invariants of the Hilbert scheme of two points in the plane. By studying the space of stable maps and computing virtual contributions, we use these invariants to enumerate hyperelliptic plane curves…
We define orbifold elliptic genus for general orbifolds which generalizes the definition of Borisov and Libgober, and prove their rigidity property.
We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…