• Corpus ID: 15209029

A simply connected numerical Godeaux surface with ample canonical class

@article{Dolgachev1997ASC,
  title={A simply connected numerical Godeaux surface with ample canonical class},
  author={Igor Dolgachev and Caryn Werner},
  journal={arXiv: Algebraic Geometry},
  year={1997}
}
We prove that a recent construction of a numerical Godeaux surface due to P. Craighero and R. Gattazzo is simply connected, and show how to realize their construction as a double plane. By proving that the surface contains no (-2)-curves, we obtain that this is the first example of a simply connected surface with vanishing geometric genus and ample canonical class. 

The Craighero–Gattazzo surface is simply connected

We show that the Craighero–Gattazzo surface, the minimal resolution of an explicit complex quintic surface with four elliptic singularities, is simply connected. This was conjectured by Dolgachev and

Canonical rings of Gorenstein stable Godeaux surfaces

Extending the description of canonical rings from Reid (J Fac Sci Univ Tokyo Sect IA Math 25(1):75–92, 1978) we show that every Gorenstein stable Godeaux surface with torsion of order at least 3 is

Bloch's conjecture on surfaces of general type with an involution

In this short note we prove that the Bloch's conjecture holds for a surface of general type of numerical Godeaux type or some class of numerical Campedelli type, with geometric genus zero equipped

Degenerations Of Godeaux Surfaces And Exceptional Vector Bundles

A recent construction of Hacking relates the classification of stable vector bundles on a surface of general type with $p_g = 0$ and the boundary of the moduli space of deformations of the surface.

Gorenstein stable Godeaux surfaces

We classify Gorenstein stable numerical Godeaux surfaces with worse than canonical singularities and compute their fundamental groups.

Geometry of quintics in $\mathbb P^3$ and the Craighero-Gattazzo surface of general type

In this paper we study the question whether the tri-canonical system on the Craighero-Gattazzo surface is base point free and at which points does it separate tangent vectors. Also we study the

Chow groups of conic bundles in $\mathbb P^5$ and the Generalised Bloch's conjecture

Consider the Fano surface of a conic bundle embedded in $\mathbb P^5$. Let $i$ denote the natural involution acting on this surface. In this note we provide an obstruction to the identity action of

A simply connected surface of general type with pg=0 and K2=2

In this paper we construct a simply connected, minimal, complex surface of general type with pg=0 and K2=2 using a rational blow-down surgery and a ℚ-Gorenstein smoothing theory.

On the class of projective surfaces of general type

Let S be a smooth complex projective surface of general type, H be a very ample divisor on S and m(S, H) be the class of (S, H). In this paper, we study a lower bound for m(S, H)− 3H2 and we improve

Generalised Bloch's conjecture on surfaces of general type with involution

In this short note we prove that an involution on certain examples of surfaces of general type with $p_g=0$, acts as identity on the Chow group of zero cycles of the relevant surface.

References

SHOWING 1-10 OF 11 REFERENCES

On the scalar curvature of Einstein manifolds

We show that there are high-dimensional smooth compact manifolds which admit pairs of Einstein metrics for which the scalar curvatures have oppo- site signs. These are counter-examples to a

A surface of general type with pg=q=0,K2=1

We construct a surface of general type with invariants \( \chi = K^2 = 1 \) and torsion group \( \Bbb{Z}/{2} \). We use a double plane construction by finding a plane curve with certain

On Campedelli branch loci

SuntoSi costruiscono nuove curve piane di ordine dieci dotate di sei punti [3, 3] che non giacciono su una conica e curve di ordine dieci dotate di cinque punti [3, 3] e di un punto quadruplo ancora

Campedelli versus Godeaux, in “Problems in the theory of surfaces and their classification

  • (Cortona,
  • 1988

Campedelli versus Godeaux, in " Problems in the theory of surfaces and their classification (Cortona, 1988)

  • Campedelli versus Godeaux, in " Problems in the theory of surfaces and their classification (Cortona, 1988)
  • 1991