The topological classification of Fano surfaces of real three-dimensional cubics

Krasnov, Vyacheslav Alekseevich

doi:10.1070/im2007v071n05abeh002377

Cited by 3 publications

(10 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Topological and deformation classification of non-singular real cubic threefolds [Kr1], [Kr2], [FK] 18 4.5. Topology of real Fano surfaces [Kr3] 19 4.6. Adjacency graphs [Kr1], [Kh] 19 4.7.…”

Section: Klein Typementioning

confidence: 99%

“…Fano surface of a 6-nodal Segre cubic threefold [Do], [HT] 49 8.3. Real Fano surfaces of one-nodal cubics [Kr3] 51 8.4. Cubic threefolds of type C 3 1.…”

Section: Klein Typementioning

confidence: 99%

“…4.5. Topology of real Fano surfaces [Kr3]. For any non-singular real threefold X of type C k , 0 k 5, the real locus of the Fano surface, F R (X) = N 5 ⊔ k+1 2 T 2 , is formed by disjoint union of k+1 2 copies of a torus (in particular, no tori for k = 0) and a non-orientable surface N 5 that is a connected sum of 5 copies of RP 2 .…”

Section: Lemma [Fi]mentioning

confidence: 99%

See 2 more Smart Citations

Deformation Classification of Real Non-singular Cubic Threefolds with a Marked Line

Finashin

Kharlamov

2018

Arnold Math J.

View full text Add to dashboard Cite

We prove that the space of pairs (X, l) formed by a real non-singular cubic hypersurface X ⊂ P 4 with a real line l ⊂ X has 18 connected components and give for them several quite explicit interpretations. The first one relates these components to the orbits of the monodromy action on the set of connected components of the Fano surface F R (X) formed by real lines on X. For another interpretation we associate with each of the 18 components a well defined real deformation class of real non-singular plane quintic curves and show that this deformation class together with the real deformation class of X characterizes completely the component.

show abstract

Section: Klein Typementioning

confidence: 99%

“…Fano surface of a 6-nodal Segre cubic threefold [Do], [HT] 49 8.3. Real Fano surfaces of one-nodal cubics [Kr3] 51 8.4. Cubic threefolds of type C 3 1.…”

Section: Klein Typementioning

confidence: 99%

See 1 more Smart Citation

Deformation Classification of Real Non-singular Cubic Threefolds with a Marked Line

Finashin

Kharlamov

2018

Arnold Math J.

View full text Add to dashboard Cite

show abstract

“…(The case of Fano surfaces of threedimensional cubics is worked out in [Kra2].) Some other relations between cubic fourfolds and K3-surfaces.…”

Section: A Few Related Remarksmentioning

confidence: 99%

“…The second question is to relate the topology of X R with the topology of the real part of the corresponding Fano varieties, which are, as is known, are nonsingular for any nonsingular cubic and hence also depend only on the coarse deformation class of the cubic. (The case of Fano surfaces of three-dimensional cubics is worked out in [Kr2].) Some other relations between cubic fourfolds and K3-surfaces.…”

Section: A Few Related Remarksmentioning

confidence: 99%

Deformation classes of real four-dimensional cubic hypersurfaces

Finashin

Kharlamov

2008

J. Algebraic Geom.

View full text Add to dashboard Cite

We study real nonsingular cubic hypersurfaces X ⊂ P 5 up to deformation equivalence combined with projective equivalence and prove that they are classified by the conjugacy classes of involutions induced by the complex conjugation in H 4 (X). Moreover, we provide a graph Γ K4 whose vertices represent the equivalence classes of such cubics and whose edges represent their adjacency. It turns out that the graph Γ K4 essentially coincides with the graph Γ K3 characterizing a certain adjacency of real nonpolarized K3-surfaces.The most familiar logics in the modal family are constructed from a weak logic called K (after Saul Kripke). Under the narrow reading, modal logic concerns necessity and possibility. A variety of different systems may be developed for such logics using K as a foundation.Stanford Encyclopedia of Philosophy, Modal Logic.

show abstract

Unexpected loss of maximality: the case of Hilbert squares of real surfaces

Kharlamov¹,

Răsdeaconu²

2023

Preprint

View full text Add to dashboard Cite

We explore the maximality of the Hilbert square of maximal real surfaces, and find that in many cases the Hilbert square is maximal if and only if the surface has connected real locus. In particular, the Hilbert square of no maximal K3-surface is maximal. Nevertheless, we exhibit maximal surfaces with disconnected real locus whose Hilbert square is maximal.On dédaigne volontiers un but qu'on n'a pas réussi à atteindre, ou qu'on a atteint définitivement.M. Proust, A la recherche du temps perdu.

show abstract

The topological classification of Fano surfaces of real three-dimensional cubics

Cited by 3 publications

References 10 publications

Deformation Classification of Real Non-singular Cubic Threefolds with a Marked Line

Deformation Classification of Real Non-singular Cubic Threefolds with a Marked Line

Deformation classes of real four-dimensional cubic hypersurfaces

Unexpected loss of maximality: the case of Hilbert squares of real surfaces

Contact Info

Product

Resources

About