Related papers: Divisor classes and the virtual canonical bundle f…

The canonical ring $S_D = \bigoplus_{d \geq 0} H^0(X, \lfloor dD \rfloor)$ of a divisor D on a curve X is a natural object of study; when D is a Q-divisor, it has connections to projective embeddings of stacky curves and rings of modular…

Let f: A\to B be a ring homomorphism between Noetherian normal integral domains. We establish a general criterion for f to induce a homomorphism Cl(f): Cl(A)\to Cl(B) on divisor class groups. For instance, this criterion applies whenever f…

We prove two results about vector bundles on singular algebraic surfaces. First, on proper surfaces there are vector bundles of rank two with arbitrarily large second Chern number and fixed determinant. Second, on separated normal surfaces…

In this mostly expository paper we review several known results about the cohomology of moduli spaces of smooth and stable curves, focusing in particular on low degree cohomology. We also give a new proof of Harer's theorem describing the…

We calculate the cycle class of the Hurwitz divisor $D_2$ on the moduli space of stable curves of genus $g=2k$ given by the degree $k+1$ covers of the projective line with simple ramification points, two of which lie in the same fibre. We…

S. Kond\=o used periods of $K3$ surfaces to prove that the moduli space of genus three curves is birational to an arithmetic quotient of a complex 6-ball. In this paper we study Heegner divisors in the ball quotient, given by arithmetically…

For a commutative ring $R$, the zero-divisor graph of $R$ is a simple graph with the vertex set as the set of all zero-divisors of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy = 0$. This article attempts to…

We study the log canonical models of the moduli space MBar_{0,n} of pointed stable genus zero curves with respect to the standard log canonical divisors K+aD, where D denotes the boundary. In particular we show that, as a formal consequence…

The aim of this paper is to present an algebro-geometric approach to the study of the geometry of the moduli space of stable bundles on a smooth projective curve defined over an algebraically closed field $k$, of arbitrary characteristic.…

Let U be a smooth quasi-projective variety over a field k that is finite, the algebraic closure of a finite field or algebraically closed of characteristic 0. Let X be a suitable projective compactification of U, and D an effective divisor…

I study a special type of canonical relations given by twisted conormal bundles, construct a "subcategory" of the symplectic "category" out of these canonical relations and quantize them into semi-classical Fourier integral operators.…

We present here some conjectures on the diagonalizability of uniform principal bundles on rational homogeneous spaces, that are natural extensions of classical theorems on uniform vector bundles on the projective space, and study the…

This paper aims at settling the issue of the validity of the de Jonqui\`eres formulas. We consider the space of divisors with prescribed multiplicity, or de Jonqui\`eres divisors, contained in a linear series on a smooth projective curve.…

Smooth surfaces have finitely generated canonical rings and projective canonical models. For normal surfaces, however, the graded ring of multicanonical sections is possibly nonnoetherian, such that the corresponding homogeneous spectrum is…

We construct a canonical correspondence from a wide class of reproducing kernels on infinite-dimensional Hermitian vector bundles to linear connections on these bundles. The linear connection in question is obtained through a pull-back…

On a stack of stable maps, the psi classes are modified by subtracting certain boundary divisors. These modified psi classes are compatible with forgetful morphisms, and are well-suited to enumerative geometry: tangency conditions allow…

Let $Y$ be an effective Cartier divisor of a smooth variety $Z$. Let $X_{i}$, $i\in \{1,\cdots,n\}$ be a set of pairwise disjoint smooth subvarieties in $Y$ such that their union contains the singular locus of $Y$. In this paper, we give a…

Let X_n := \bar M_{0,n}, the moduli space of n-pointed stable genus zero curves, and let X_{n,m} be the quotient of X_n by the action of the symmetric group S_{n-m} on the last n-m marked points. The cones of effective divisors of X_{n,m},…

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

We investigate the orientability of a class of vector bundles over flag manifolds of real semi-simple Lie groups, which include the tangent bundle and also stable bundles of certain gradient flows. Closed formulas, in terms of roots, are…