28 citations · 136 across the 17 of their papers we have counts for
17 papers
Roughness spectroscopy of particle monolayer: Implications for spectral analysis of the monolayer image
Paweł Weroński, Karolina Pałka
Surface roughness of particle monolayer is one of its fundamental characteristics, conventionally described in terms of power spectral density. We derive a general equation for thi…
Completions of affine spaces into Mori fiber spaces with non-rational fibers
Adrien Dubouloz, Takashi Kishimoto, Karol Palka
We describe a method to construct completions of affine spaces into total spaces of -factorial terminal Mori fiber spaces over the projective line. As an application we…
Complex planar curves homeomorphic to a line have at most four singular points
Mariusz Koras, Karol Palka
We show that a complex planar curve homeomorphic to the projective line has at most four singular points. If it has exactly four then it has degree five and is unique up to a proje…
Classification of planar rational cuspidal curves. II. Log del Pezzo models
Karol Palka, Tomasz Pełka
Let be a complex curve homeomorphic to the projective line. The Negativity Conjecture asserts that the Kodaira-Iitaka dimension of , whe…
The Jacobian Conjecture fails for pseudo-planes
Adrien Dubouloz, Karol Palka
A smooth complex variety satisfies the Generalized Jacobian Conjecture if all its étale endomorphisms are proper. We study the conjecture for -acyclic surfaces of negat…
Classification of planar rational cuspidal curves. I. C**-fibrations
Karol Palka, Tomasz Pełka
To classify complex rational cuspidal curves it remains to classify the ones with complement of log general type, i.e. the ones for which , wh…
The Coolidge-Nagata conjecture
Mariusz Koras, Karol Palka
Let be a complex rational cuspidal curve contained in the projective plane. The Coolidge-Nagata conjecture asserts that is Cremona equivalent to a lin…
The geometry of sporadic -embeddings into
Mariusz Koras, Karol Palka, Peter Russell
A closed algebraic embedding of into is 'sporadic' if for every curve isomorphic to an affine lin…
The Coolidge-Nagata conjecture, part I
Karol Palka
Let be a complex rational cuspidal curve contained in the projective plane and let be the minimal log resolution of singularit…
A new proof of the theorems of Lin-Zaidenberg and Abhyankar-Moh-Suzuki
Karol Palka
Using the theory of minimal models of quasi-projective surfaces we give a new proof of the theorem of Lin-Zaidenberg which says that every topologically contractible algebraic curv…
Cuspidal curves, minimal models and Zaidenberg's finiteness conjecture
Karol Palka
Let be a complex rational cuspidal curve and let be the minimal log resolution of singularities. We prove that has at…
The Coolidge-Nagata conjecture holds for curves with more than four cusps
Karol Palka
Let E be a plane rational curve defined over complex numbers which has only locally irreducible singularities. The Coolidge-Nagata conjecture states that E is rectifiable, i.e. it…
Classification of singular Q-homology planes. II. C^1- and C*-rulings
Karol Palka
A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We classify singular Q-homology planes which are C^1- or C*-ruled. We analyze their compl…
Recent progress in the geometry of Q-acyclic surfaces
Karol Palka
We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.
Singular Q-homology planes of negative Kodaira dimension have smooth locus of non-general type
Karol Palka, Mariusz Koras
We continue the program of classification of normal Q-acyclic surfaces defined over the field of complex numbers, so-called 'Q-homology planes'. Here we show that if a Q-homology p…
Exceptional singular Q-homology planes
Karol Palka
We consider singular Q-acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is C^1- or C*-rul…
Classification of singular Q-homology planes. I. Structure and singularities
Karol Palka
A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type…