We study the enumerative geometry of algebraic curves on abelian surfaces and threefolds.
In the abelian surface case, the theory is parallel to the well-developed study of the reduced …

We complete the remaining cases of the conjecture predicting existence of infinitely many
rational curves on K3 surfaces in characteristic 0, prove almost all cases in positive …

Rational curves on Hilbert schemes of points on $ K3 $ surfaces and generalised Kummer
manifolds are constructed by using Brill–Noether theory on nodal curves on the underlying …

Curve classes on irreducible holomorphic symplectic varieties Page 1 Communications in
Contemporary Mathematics Vol. 22, No. 7 (2020) 1950078 (15 pages) c World Scientific …

arXiv:2406.19993v1 [math.AG] 28 Jun 2024 Page 1 arXiv:2406.19993v1 [math.AG] 28 Jun 2024
DISTINGUISHING BRILL–NOETHER LOCI ASHER AUEL, RICHARD HABURCAK, AND …

Using lattice theory, Hulek and Sch\" utt proved that for every $ m\in\mathbb {Z} _+ $ there
exists a nine-dimensional family $\mathcal {F} _m $ of K3 surfaces covering Enriques …

Let be a general polarised Enriques surface, with L not numerically 2-divisible. We prove the
existence of regular components of all Severi varieties of irreducible nodal curves in the …

Severi varieties are roughly moduli spaces of curves of a fixed homology class and
geometric genus on a projective surface. In this paper, we determine the irreducible …

Let $(S, L) $ be a general primitively polarized $ K3 $ surface of genus $ g $. For every
$0\leq\delta\leq g $ we consider the Severi variety parametrizing integral curves in $| L …

Chen-Gounelas-Liedtke recently introduced a powerful regeneration technique, a process
opposite to specialization, to prove existence results for rational curves on projective …