On the number of singular points of terminal factorial Fano threefolds

Prokhorov, Yuri

doi:10.1134/s0001434617050364

Cited by 17 publications

(10 citation statements)

References 10 publications

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“…V 5 be a double cover branched over a surface S 2 j K V 5 j. If S has an isolated ordinary double point, then X is rationally connected [215], it is Q-factorial [50], and it follows from [183] that there exists the following Sarkisov link:…”

Section: Cylindrical Fano Threefoldsmentioning

confidence: 99%

Cylinders in Fano varieties

Cheltsov

Park

Prokhorov

et al. 2021

EMS Surv. Math. Sci.

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Section: Cylindrical Fano Threefoldsmentioning

confidence: 99%

Cylinders in Fano varieties

Cheltsov

Park

Prokhorov

et al. 2021

EMS Surv. Math. Sci.

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“…If Y is sufficiently general, then by blowing up Π we obtain a standard conic bundle over P 2 with discriminant curve of degree 7, see e.g. [ [Pro17]). Let ϕ : Y → P 3 be a double cover branched over a quartic surface B ⊂ P 3 .…”

Section: Conic Bundlesmentioning

confidence: 99%

The rationality problem for conic bundles

Prokhorov¹

2018

Russ. Math. Surv.

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“…Relation to other work. Gorenstein terminal del Pezzo threefolds specifically have been studied by Prokhorov [25,27], where he sometimes blows up nodal (resp. lci) curves to produce nodal (resp.…”

Section: Introductionmentioning

confidence: 99%

Derived categories of nodal del Pezzo threefolds

Pavic,

Shinder

2021

Preprint

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We give a complete answer for the existence of Kawamata type semiorthogonal decompositions of derived categories of nodal del Pezzo threefolds. More precisely, we show that nodal non smooth V d with 1 ≤ d ≤ 4 have no Kawamata type decomposition and that all nodal V5 admit a Kawamata decomposition. For the proof we go through the classification of singular del Pezzo threefolds, compute divisor class groups of nodal del Pezzo threefolds of small degree and use projection from a line to construct Kawamata semiorthogonal decompositions for d = 5. A Kawamata decomposition of nodal V6 has been previously constructed in [13].

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On the number of singular points of terminal factorial Fano threefolds

Cited by 17 publications

References 10 publications

Cylinders in Fano varieties

Cylinders in Fano varieties

The rationality problem for conic bundles

Derived categories of nodal del Pezzo threefolds

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