# On the irreducibility of Hilbert scheme of surfaces of minimal degree

Fedor Bogomolov; Viktor Kulikov

Open Mathematics (2013)

- Volume: 11, Issue: 2, page 254-263
- ISSN: 2391-5455

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topFedor Bogomolov, and Viktor Kulikov. "On the irreducibility of Hilbert scheme of surfaces of minimal degree." Open Mathematics 11.2 (2013): 254-263. <http://eudml.org/doc/268943>.

@article{FedorBogomolov2013,

abstract = {The article contains a new proof that the Hilbert scheme of irreducible surfaces of degree m in ℙm+1 is irreducible except m = 4. In the case m = 4 the Hilbert scheme consists of two irreducible components explicitly described in the article. The main idea of our approach is to use the proof of Chisini conjecture [Kulikov Vik.S., On Chisini’s conjecture II, Izv. Math., 2008, 72(5), 901–913 (in Russian)] for coverings of projective plane branched in a special class of rational curves.},

author = {Fedor Bogomolov, Viktor Kulikov},

journal = {Open Mathematics},

keywords = {Hilbert scheme; Irreducible projective algebraic surfaces of minimal degree; irreducible surfaces of minimal degree; coverings of the plane},

language = {eng},

number = {2},

pages = {254-263},

title = {On the irreducibility of Hilbert scheme of surfaces of minimal degree},

url = {http://eudml.org/doc/268943},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Fedor Bogomolov

AU - Viktor Kulikov

TI - On the irreducibility of Hilbert scheme of surfaces of minimal degree

JO - Open Mathematics

PY - 2013

VL - 11

IS - 2

SP - 254

EP - 263

AB - The article contains a new proof that the Hilbert scheme of irreducible surfaces of degree m in ℙm+1 is irreducible except m = 4. In the case m = 4 the Hilbert scheme consists of two irreducible components explicitly described in the article. The main idea of our approach is to use the proof of Chisini conjecture [Kulikov Vik.S., On Chisini’s conjecture II, Izv. Math., 2008, 72(5), 901–913 (in Russian)] for coverings of projective plane branched in a special class of rational curves.

LA - eng

KW - Hilbert scheme; Irreducible projective algebraic surfaces of minimal degree; irreducible surfaces of minimal degree; coverings of the plane

UR - http://eudml.org/doc/268943

ER -

## References

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- [7] Kulikov Vik.S., A remark on classical Pluecker’s formulae, preprint available at http://arxiv.org/abs/1101.5042
- [8] Kulikov V.S., Kulikov Vik.S., On complete degenerations of surfaces with ordinary singularities in ℙ3, Sb. Math., 2010, 201(1), 129–158 http://dx.doi.org/10.1070/SM2010v201n01ABEH004068
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- [11] Shafarevich I.R., Averbukh B.G., Vainberg Yu.R., Zhizhchenko A.B., Manin Yu.I., Moishezon B.G., Tyurina G.N., Tyurin A.N., Algebraic Surfaces, Trudy Mat. Inst. Steklov., 75, Nauka, Moscow, 1965 (in Russian)

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