Related papers: R-Matrix Structure of Hitchin System in Tyurin Par…

Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \chi of P. We prove that a holomorphic principal G-bundle E over a connected complex…

We give an algebraic approach to the study of Hitchin pairs and prove the tensor product theorem for Higgs semistable Hitchin pairs over smooth projective curves defined over algebraically closed fields $k$ of characteristic $0$ and…

In algebraic geometry, it is important to provide effective parametrizations for families of curves, both in theory and in practice. In this paper, we present such an effective parametrization for the moduli of genus-$5$ curves that are…

For G = GL_2, PGL_2 and SL_2 we prove that the perverse filtration associated to the Hitchin map on the cohomology of the moduli space of twisted G-Higgs bundles on a Riemann surface C agrees with the weight filtration on the cohomology of…

We obtain non-trivial solutions to the heterotic $\rm{G}_2$ system, which are defined on the total spaces of non-trivial circle bundles over Calabi--Yau $3$-orbifolds. By adjusting the $S^1$ fibres in proportion to a power of the string…

Let $X$ be a smooth irreducible projective curve. Recently, Pauly and Pe\'on-Nieto shows that a vector bundle over $X$ is very stable if and only if the Hitchin map on the vector space of Higgs field on that vector bundle is proper. In this…

The paper studies explicitly the Hitchin system restricted to the Higgs fields on a fixed very stable rank 2 bundle in genus 2 and 3. The associated families of quadrics relate to both the geometry of Penrose's twistor spaces and several…

For a regular pair $(X,Y)$ of schemes of pure codimension 1 on which 2 is invertible, we consider quadric bundles on $X$ which are nondegenerate on $X-Y$, but are minimally degenerate on $Y$. We give a formula for the behaviour of the…

We provide a general method for constructing moduli stacks whose points are diagrams of vector bundles over a fixed base, indexed by a fixed simplicial set -- that is, quiver bundles of a fixed shape. We discuss some constraints on the base…

A new construction is given for obtaining R-matrices which solve the McGuire-Yang-Baxter equation in such a way that the spectral parameters do not possess the difference property. A discussion of the derivation of the supersymmetric U…

We construct a smooth Artin stack parameterizing the stable weighted curves of genus one with twisted fields and prove that it is isomorphic to the blowup stack of the moduli of genus one weighted curves studied by Hu and Li. This leads to…

In this paper we show that a surface in P^3 parametrized over a 2-dimensional toric variety T can be represented by a matrix of linear syzygies if the base points are finite in number and form locally a complete intersection. This…

This paper shows that the Hodge bundle over the moduli space of genus $g \geq 2$ curves does not contain any non-trivial sub-bundles. Notably, the mathematical content was generated by Aletheia, a custom AI agent powered by Gemini Deep…

There are families of physical systems that cannot be adiabatically evolved to the trivial system uniformly across the parameter space, even if each system in the family belongs to the trivial phase. The obstruction is measured by higher…

In this paper we continue our studies of Hitchin systems on singular curves (started in hep-th/0303069). We consider a rather general class of curves which can be obtained from the projective line by gluing two subschemes together (i.e.…

We study the hyperk\"ahler analogues of moduli spaces of semistable n-gons in complex projective space. We prove that the hyperk\"ahler Kirwan map is surjective and produce a formula that recursively calculates the Betti numbers of these…

The existence problem for vector bundles on a smooth compact complex surface consists in determining which topological complex vector bundles admit holomorphic structures. For projective surfaces, Schwarzenberger proved that a topological…

We construct families of smooth, proper, algebraic curves in characteristic 0, of arbitrary genus g, together with g elements in the kernel of the tame symbol. We show that those elements are in general independent by a limit calculation of…

Prior works relating meromorphic Higgs bundles to topological recursion, in particular those of Dumitrescu-Mulase, have considered non-singular models that allow the recursion to be carried out on a smooth Riemann surface. We start from an…

A geometric algorithm is introduced for finding a symplectic basis of the first integral homology group of a compact Riemann surface, which is a $p$-cyclic covering of ${\mathbb C} P^1$ branched over 3 points. The algorithm yields a…