Related papers: Positivity of divisor classes on the strata of dif…

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…

Using the duality of positive cones, we show that applying the polar transform from convex analysis to local positivity invariants for divisors gives interesting and new local positivity invariants for curves. These new invariants have nice…

In this papers, we study the geometric and arithmetic properties of the theta divisor associated to the sheaf of locally exact differential forms over a curve in positive characteristic. In this published version, we prove a stronger…

We prove two statements on the slopes of effective divisors on the moduli space of stable curves of genus g: first that the Harris-Morrison Slope Conjecture fails for g=10 and second, that in order to compute the slope of the moduli space…

We establish a new moduli theory for divisors, that interpolates between the Hilbert scheme and the Cayley-Chow variety. This completes the last step in the construction of a good moduli theory for stable pairs $(X,\Delta)$.

In this thesis we prove Schur-positivity of certain graph families. In addition, we exlpor existence of cyclic descent extensions on several families of Schur-positive sets.

We propose a general method to construct new triangulated categories, relative stable categories, as additive quotients of a given one. This construction enhances results of Beligiannis, particularly in the tensor-triangular setting. We…

We prove that a triangulated category which is the underlying category of a stable derivator has a filtered enhancement, providing an affirmative answer to a conjecture in [3].

We prove relations among the classes of certain divisors on the moduli spaces of curves with marked points, generalizing the Brill-Noether Ray Theorem of Eisenbud and Harris.

We study some examples of Bridgeland-Douglas stability conditions on triangulated categories. From one side we give a complete description of the stability manifolds for smooth projective curves of positive genus. From the other side we…

We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…

We study concepts of stabilities associated to a smooth complex curve together with a linear series on it. In particular we investigate the relation between stability of the associated Dual Span Bundle and linear stability. Our result…

For a hyperelliptic curve of genus $g$, a divisor in general position of degree $g+1$ is given by polynomial equations. There is an action from an algebraic group on the representations of divisors by polynomials which fixes divisor…

In a previous joint article with F. Abu Salem, we gave efficient algorithms for Jacobian group arithmetic of "typical" divisor classes on C_{3,4} curves, improving on similar results by other authors. At that time, we could only state that…

We prove a sharp relative Clifford inequality for relatively special divisors on varieties fibered by curves. It generalizes the classical Clifford inequality about a single curve to a family of curves. It yields a geographical inequality…

We show that the homology of strata of abelian differentials stabilizes in a range where the number of simple zeros is large relative to the homological degree. In this range, we show that the rational cohomology agrees with the restriction…

We give a stack-theoretic proof for some results on families of hyperelliptic curves.

We show that positivity of the CM line associated to a family of polarised varieties is intimately related to the stability of its members. We prove that the CM line is nef on any curve which meets the stable locus, and that it is…

Let $X$ be a complex nonsingular variety with globally generated tangent bundle. We prove that the signed Segre-MacPherson (SM) class of a constructible function on $X$ with effective characteristic cycle is effective. This observation has…

For $g\geq2$, $j=1,\dots,g$ and $n\geq g+j$ we exhibit infinitely many new rigid and extremal effective codimension $j$ cycles in $\overline{\mathcal{M}}_{g,n}$ from the strata of quadratic differentials and projections of these strata…