Related papers: Towards Fulton's conjecture

We prove the famous Faber intersection number conjecture and other more general results by using a recursion formula of $n$-point functions for intersection numbers on moduli spaces of curves. We also present some vanishing properties of…

This is a continuation of "Rational families of vector bundles on curves, I". Let C be a smooth projective curve of genus at least 2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1.…

By using classical invariant theory, we reduce the $S_{n}$-invariant F-conjecture to a feasibility problem in polyhedral geometry. We show by computer that for $n \le 19$, every integral $S_{n}$-invariant F-nef divisor on the moduli space…

We introduce and study smooth compactifications of the moduli space of n labeled points with weights in projective space, which have normal crossings boundary and are defined as GIT quotients of the weighted Fulton-MacPherson…

The purpose of this note is to announce our proof of the Atiyah-Jones conjecture concerning the topology of the moduli spaces of based SU(2)-instantons over S^4. Full details and proofs appear in our paper [BHMM1].

We shall prove that a moduli space of flat irreducible Lie algebroid connections over a compact manifold has locally a natural structure of a smooth differentiable space. This is a generalization of some well known results for the moduli…

We revisit moduli stabilization on Calabi-Yau manifolds with a discrete symmetry. Invariant fluxes allow for a truncation to a symmetric locus in complex structure moduli space and hence drastically reduce the moduli stabilization problem…

Given an integer $\gamma\geq 2$ and an odd prime power $q$ we show that for every large genus $g$ there exists a non-singular curve $C$ defined over $\mathbb{F}_q$ of genus $g$ and gonality $\gamma$ and with exactly $\gamma(q+1)$…

We prove that the moduli space of curves with level structures has an enormous amount of rational cohomology in its cohomological dimension. As an application, we prove that the coherent cohomological dimension of the moduli space of curves…

Let $M_{g, n}$ (respectively, $\overline{M_{g, n}}$) be the moduli space of smooth (respectively stable) curves of genus $g$ with $n$ marked points. Over the field of complex numbers, it is a classical problem in algebraic geometry to…

We introduce and motivate a conjecture about the existence of complete, 1-dimensional families of covers of an elliptic curve. If the conjecture holds, then it would imply a uniform lower bound of 5 for slope of the moduli space of curves.…

We establish asymptotic formulas for counting rational points near finite type curves on the plane, generalizing Huang's result.

We give two proofs that appropriately defined congruence subgroups of the mapping class group of a surface with punctures/boundary have enormous amounts of rational cohomology in their virtual cohomological dimension. In particular we give…

In the present paper, we study a new kind of anabelian phenomenon concerning the smooth pointed stable curves in positive characteristic. It shows that the topological structures of moduli spaces of curves can be understood from the…

We show the properness of the moduli stack of stable surfaces over $\mathbb{Z}[1/30]$, assuming the locally-stable reduction conjecture for stable surfaces. This relies on a local Kawamata--Viehweg vanishing theorem for for 3-dimensional…

We sharpen our previous results on the g and n such that the moduli space of curves of genus g with n marked points is of general type.

The enumerative geometry of r-th roots of line bundles is the subject of Witten's conjecture and occurs in the calculation of Gromov-Witten invariants of orbifolds. It requires the definition of the suitable compact moduli stack and the…

Let X be a smooth projective curve of genus g \geq 2 defined over a field of characteristic two. We give examples of stable orthogonal bundles with unstable underlying vector bundles and use them to give counterexamples to Behrend's…

Let C be a smooth projective curve of genus at least 2 over a field k. Given a line bundle L on C, we consider the moduli stack of rank 2n vector bundles E on C endowed with a nowhere degenerate symplectic form $b: E \otimes E \to L$ up to…

We propose an approach for showing rationality of an algebraic variety $X$. We try to cover $X$ by rational curves of certain type and count how many curves pass through a generic point. If the answer is $1$, then we can sometimes reduce…