Irregular surfaces on hypersurfaces of degree 4 with non-degenerate isolated singularities
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Daniel Naie
Abstract
It is shown that a smooth surface lying on a nodal quartic hypersurface in ℙ4 is either regular or an elliptic conic bundle of degree 8. Furthermore, the latter configuration is shown to exist.
Communicated by: C. Scheiderer
Acknowledgements
This is the second paper that originates from the work [17] Igor Reider and myself archived in 2016. I would like to express my gratitude to Igor for the moments we shared trying to understand the geometry of surfaces in ℙ4, to Laurent Gruson for the many e-conversations we had concerning the rich geometry of Cremona transformations of ℙ4 and of Segre cubics, and to Stéphane Druel and Jean-Philippe Monnier for the discussions around Lemma 4.5. Finally, I would like to thank the referee for the constructive criticism on questions of presentation and the suggestion to use Macaulay 2 to prove the existence of the nodal quartic in Proposition 4.4.
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Articles in the same Issue
- Frontmatter
- The Malgrange–Galois groupoid of the Painlevé VI equation with parameters
- Explicit Nikulin configurations on Kummer surfaces
- Irregular surfaces on hypersurfaces of degree 4 with non-degenerate isolated singularities
- Counting isolated points outside the image of a polynomial map
- An inverse approach to hyperspheres of prescribed mean curvature in Euclidean space
- Bridgeland stability conditions on surfaces with curves of negative self-intersection
- Computation of Dressians by dimensional reduction
- A few more extensions of Putinar’s Positivstellensatz to non-compact sets
- On the Jacobian locus in the Prym locus and geodesics
- Weierstrass semigroups for maximal curves realizable as Harbater–Katz–Gabber covers
Articles in the same Issue
- Frontmatter
- The Malgrange–Galois groupoid of the Painlevé VI equation with parameters
- Explicit Nikulin configurations on Kummer surfaces
- Irregular surfaces on hypersurfaces of degree 4 with non-degenerate isolated singularities
- Counting isolated points outside the image of a polynomial map
- An inverse approach to hyperspheres of prescribed mean curvature in Euclidean space
- Bridgeland stability conditions on surfaces with curves of negative self-intersection
- Computation of Dressians by dimensional reduction
- A few more extensions of Putinar’s Positivstellensatz to non-compact sets
- On the Jacobian locus in the Prym locus and geodesics
- Weierstrass semigroups for maximal curves realizable as Harbater–Katz–Gabber covers
