Related papers: Dalian notes on rational Pontryagin classes

Refinements of the Yang-Mills stratifications of spaces of connections over a compact Riemann surface are investigated. The motivation for this study was the search for a complete set of relations between the standard generators for the…

We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential…

We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belongs to a different…

Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…

Let Mod_g be the mapping class group of a genus g >= 2 surface. The group Mod_g has virtual cohomological dimension 4g-5. In this note we use a theorem of Broaddus and the combinatorics of chord diagrams to prove that H^{4g-5}(Mod_g; Q) =…

Yanchevski\u{i} had asked whether conic bundle surfaces over $\mathbf{P}^1_k$ are unirational when $k$ is a finite field. We give a partial answer to his question by showing that for quasi-finite fields $k$ (e.g. finite fields) a regular…

We give a formula comparing the E-series of the moduli stacks of rank 2 degree 0 semistable Higgs bundles in genus $g \geq 2$ to intersection E-polynomials of its coarse moduli space. A parellel formula holds in various 2-Calabi-Yau…

Co-Higgs bundles are Higgs bundles in the sense of Simpson, but with Higgs fields that take values in the tangent bundle instead of the cotangent bundle. Given a vector bundle on P^1, we find necessary and sufficient conditions on its…

Let $C$ be a chain-like curve over $\mathbb{C}$. In this paper, we investigate the rationality of moduli spaces of $w$-semistable vector bundles on $C$ of arbitrary rank and fixed determinant by putting some restrictions on the Euler…

Let $M(2,\textbf{\underline{w}},\chi)$ be the moduli space of rank $2$ torsion-free sheaves over a reducible nodal curve with each component having utmost two nodal singularities. We show that in each component of…

We study the space $\nua{m}{d}$ of clouds in $\bbr^d$ (ordered sets of $m$ points modulo the action of the group of affine isometries). We show that $\nua{m}{d}$ is a smooth space, stratified over a certain hyperplane arrangement in…

We study the category whose objects are trees (with or without roots) and whose morphisms are contractions. We show that the corresponding contravariant module categories are Noetherian, and we study two natural families of modules over…

We prove three results on pure resolutions of vector bundles on projective spaces. First, we show that there are simple vector bundles of rank n on Pn with arbitrary homological dimension. We then analyze the pure resolutions given by the…

We study vector bundles on curves with rational tails and their smoothings and give a sufficient condition for the general fibre to be balanced.

We prove that any rational linear combination of Pontryagin numbers that does not factor through the universal elliptic genus is unbounded on connected closed spin manifolds of nonnegative sectional curvature.

We construct Abelian model structures on the category of chain complexes over a ring $R$, from the notion homological dimensions of modules. Given an integer $n > 0$, we prove that the left modules over a ringoid $\mathfrak{R}$ with…

This paper is the second in a series of three devoted to the smooth classification of simply connected elliptic surfaces. In this paper, we study the case where one of the multiple fibers has even multiplicity, and describe the moduli space…

In this paper I consider a quintic surface in $\pp^3$, general in the sense of Noether-Lefschetz theory. The vector bundles of rank 2 on this surface which are $\mu$-stable with respect to the hyperplane section and have $c_1 = K$, the…

Let ${\mathbb F}_0$ be an algebraically closed field, with $char({\mathbb F}_0)=0$. In this article, for prime numbers $p\geq 2$, we construct smooth affine algebras $B$ over ${\mathbb F}_0$, with $\dim B=p+2$. Further, we construct…

We argue that modular classes of Q-manifolds provide an efficient method for addressing the existence of supersymmetric Berezin volumes in the supergeometric representation theory of the $\mathcal{N}=2$ $d=1$ supertranslation algebra. We…