3 citations · 5 across the 10 of their papers we have counts for
13 papers
Multiscale differentials and wonderful models
Prabhat Devkota, Antonios-Alexandros Robotis, Adrian Zahariuc
We study the relationships between several varieties parametrizing marked curves with differentials in the literature. More precisely, we prove that the space of mu…
Severi Varieties on Ruled Surfaces over Elliptic Curves
Xiaotian Chang, Xi Chen, Adrian Zahariuc
We proved that the general members of Severi varieties on an Atiyah ruled surface over a general elliptic curve have nodes and ordinary triple points as singularities.
Interpolation of fat points on K3 and abelian surfaces
Adrian Zahariuc
We prove that any number of general fat points of any multiplicities impose the expected number of conditions on a linear system on a smooth projective surface, in several cases in…
Small resolutions of moduli spaces of scaled curves
Adrian Zahariuc
We construct small resolutions of the moduli space of stable scaled -marked lines of Ziltener and Ma'u--Woodward and of the moduli space of sta…
Marked nodal curves with vector fields
Adrian Zahariuc
We discuss two operations on nodal curves with (logarithmic) vector fields, which resemble the `stabilization' construction in Knudsen's proof that is th…
Configurations of points on a line up to scaling or translation
Adrian Zahariuc
We prove that the Losev--Manin compactification of the space of configurations of points on modulo scaling degenerates (isotrivially) to…
The Severi problem for abelian surfaces in the primitive case
Adrian Zahariuc
We prove that the irreducible components of primitive class Severi varieties of general abelian surfaces are completely determined by the maximal factorization through an isogeny o…
A Riemann-Hurwitz-Plucker formula
Brian Osserman, Adrian Zahariuc
We prove a simultaneous generalization of the classical Riemann-Hurwitz and Plucker formulas, addressing the total inflection of a morphism from a (smooth, projective) curve to an…
Reducible Calabi-Yau threefolds with countably many rational curves
Adrian Zahariuc
We give a class of examples of reducible (d-semistable) threefolds of CY type with two irreducible components for which (it is reasonably easy to prove that) no family of admissibl…
The irreducibility of the generalized Severi varieties
Adrian Zahariuc
We give an inductive proof that the generalized Severi varieties -- the varieties which parametrize (irreducible) plane curves of given degree and genus, with a fixed tangency prof…
Elliptic surfaces and linear systems with fat points
Adrian Zahariuc
We investigate the expected dimensionality of linear systems with general fat points on certain surfaces using an approach by specialization to elliptic surfaces. For the projectiv…
Rational Curves on Del Pezzo Manifolds
Adrian Zahariuc
We exploit an elementary specialization technique to study some properties of rational curves on index Fano -folds. We prove a simple formula for counting rational curves…
Deformation of Quintic Threefolds to the Chordal Variety
Adrian Zahariuc
We consider a family of quintic threefolds specializing to a certain reducible threefold. We describe the space of genus zero stable morphisms to the central fiber (as defined by J…