Heegaard Floer homology and rational cuspidal curves
M Borodzik, C Livingston - Forum of Mathematics, Sigma, 2014 - cambridge.org
We apply the methods of Heegaard Floer homology to identify topological properties of
complex curves in. As one application, we resolve an open conjecture that constrains the …
complex curves in. As one application, we resolve an open conjecture that constrains the …
On free curves and related open problems
A Dimca - arXiv preprint arXiv:2312.07591, 2023 - arxiv.org
In this paper we collect the main properties of free curves in the complex projective plane
and a lot of conjectures and open problems, both old and new. In the quest to understand …
and a lot of conjectures and open problems, both old and new. In the quest to understand …
Graded roots and singularities
A Némethi - Singularities in geometry and topology, 2007 - World Scientific
The present article aims to discuss the graded roots introduced by the author in his study of
the topology of normal surface singularities. In the body of the paper we emphasize two …
the topology of normal surface singularities. In the body of the paper we emphasize two …
Ellipsoidal superpotentials and stationary descendants
G Mikhalkin, K Siegel - arXiv preprint arXiv:2307.13252, 2023 - arxiv.org
We compute stationary gravitational descendants in symplectic ellipsoids of any dimension,
and use these to derive a number of new recursive formula for punctured curve counts in …
and use these to derive a number of new recursive formula for punctured curve counts in …
Free divisors and rational cuspidal plane curves
A Dimca, G Sticlaru - arXiv preprint arXiv:1504.01242, 2015 - arxiv.org
arXiv:1504.01242v4 [math.AG] 1 May 2015 Page 1 arXiv:1504.01242v4 [math.AG] 1 May
2015 FREE DIVISORS AND RATIONAL CUSPIDAL PLANE CURVES ALEXANDRU DIMCA1 …
2015 FREE DIVISORS AND RATIONAL CUSPIDAL PLANE CURVES ALEXANDRU DIMCA1 …
On some conjectures about free and nearly free divisors
E Artal Bartolo, L Gorrochategui, I Luengo… - … and Computer Algebra …, 2017 - Springer
In this paper we provide infinite families of non-rational irreducible free divisors or nearly
free divisors in the complex projective plane. Moreover, their corresponding local …
free divisors in the complex projective plane. Moreover, their corresponding local …
The symplectic isotopy problem for rational cuspidal curves
M Golla, L Starkston - Compositio Mathematica, 2022 - cambridge.org
We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those
whose singularities are modeled on complex curve singularities. We study the …
whose singularities are modeled on complex curve singularities. We study the …
The Coolidge–Nagata conjecture
M Koras, K Palka - 2017 - projecteuclid.org
Abstract Let E⊆ P 2 be a complex rational cuspidal curve contained in the projective plane.
The Coolidge–Nagata conjecture asserts that E is Cremona-equivalent to a line, that is, it is …
The Coolidge–Nagata conjecture asserts that E is Cremona-equivalent to a line, that is, it is …
On rational cuspidal projective plane curves
JF De Bobadilla, I Luengo-Velasco… - Proceedings of the …, 2006 - cambridge.org
In 2002, L. Nicolaescu and the fourth author formulated a very general conjecture which
relates the geometric genus of a Gorenstein surface singularity with rational homology …
relates the geometric genus of a Gorenstein surface singularity with rational homology …
Ellipsoidal superpotentials and singular curve counts
D McDuff, K Siegel - arXiv preprint arXiv:2308.07542, 2023 - arxiv.org
Given a closed symplectic manifold, we construct invariants which count (a) closed rational
pseudoholomorphic curves with prescribed cusp singularities and (b) punctured rational …
pseudoholomorphic curves with prescribed cusp singularities and (b) punctured rational …