Moduli of Prym curves.
Moduli of Vector Bundles on Curves with Parabolic Structures.
Moduli Spaces for Real Algebraic Curves and Real Abelian Varieties.
Moduli spaces of (semi)stable vector bundles on tree-linke curves.
Modulprobleme in der algebraischen Geometrie III
Multiple zeta values and periods of moduli spaces
We prove a conjecture due to Goncharov and Manin which states that the periods of the moduli spaces of Riemann spheres with marked points are multiple zeta values. We do this by introducing a differential algebra of multiple polylogarithms on and proving that it is closed under the operation of taking primitives. The main idea is to apply a version of Stokes’ formula iteratively to reduce each period integral to multiple zeta values. We also give a geometric interpretation of the double shuffle...
Nodal Cubic Surfaces and the Rationality of the Moduli Space of Curves of Genus Two.
Noether-Lefschetz, space curves and mathematical instantons.
Non-primitive linear systems on smooth algebraic curves and a generalization of Maroni theory.
Non-simple semistable vector bundles over a curve.
Normal bundle to curves in quadrics
Normal forms and moduli spaces of curve singularities with semigroup
Number of moduli of ireducible families of plane curves with nodes and cusps.
Obstructions to deforming curves on a -fold, II: Deformations of degenerate curves on a del Pezzo -fold
We study the Hilbert scheme of smooth connected curves on a smooth del Pezzo -fold . We prove that any degenerate curve , i.e. any curve contained in a smooth hyperplane section of , does not deform to a non-degenerate curve if the following two conditions are satisfied: (i) and (ii) for every line on such that , the normal bundle is trivial (i.e. ). As a consequence, we prove an analogue (for ) of a conjecture of J. O. Kleppe, which is concerned with non-reduced components...
On a Theorem of Castelnuovo, and the Equations Defining Space Curves.
On algebraic points on curves
On Castelnuovo's equivalence defect.
On curves with a theta-characteristic whose space of sections has dimension 4.
On Dimension Theorems of the Varieties of Special Divisors on a Curve.
On Linearly Normal Space Curves.