Which quartic double solids are rational?

Cheltsov, Ivan; Przyjalkowski, Victor; Shramov, Constantin

doi:10.1090/jag/730

Cited by 25 publications

(17 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this case, if H 3 6 3, then X is irrational (see [6,42,48,87,88,210]), so that it is not cylindrical. On the other hand, if H 3 > 4, then X contains a .…”

Section: Cylindrical Fano Threefoldsmentioning

confidence: 99%

Cylinders in Fano varieties

Cheltsov

Park

Prokhorov

et al. 2021

EMS Surv. Math. Sci.

Self Cite

View full text Add to dashboard Cite

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

show abstract

“…In this case, if H 3 6 3, then X is irrational (see [6,42,48,87,88,210]), so that it is not cylindrical. On the other hand, if H 3 > 4, then X contains a .…”

Section: Cylindrical Fano Threefoldsmentioning

confidence: 99%

Cylinders in Fano varieties

Cheltsov

Park

Prokhorov

et al. 2021

EMS Surv. Math. Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…This implies that π1(Bun s (C/ι)) coincides with the fundamental group of a (small) resolution of Bun ss (C/ι). Further, Bun ss (C/ι) is rational by [46,Theorem 2.2] or [8,Theorem 1.3]; see also [43, §5.4.2 and §5.5], where a small resolution of Bun ss (C/ι) is denoted Bun ss…”

Section: Quasi-étale Covers Of M Dol (X Sl N )mentioning

confidence: 99%

P=W conjectures for character varieties with symplectic resolution

Felisetti¹,

Mauri²

2020

Preprint

View full text Add to dashboard Cite

We establish P=W and PI=WI conjectures for character varieties with structural group GLn and SLn which admit a symplectic resolution, i.e. for genus 1 and arbitrary rank, and genus 2 and rank 2. We formulate the P=W conjecture for resolution, and prove it for symplectic resolutions. We exploit the topology of birational and quasi-étale modifications of Dolbeault moduli spaces of Higgs bundles. To this end, we prove auxiliary results of independent interest, like the construction of a relative compactification of the Hodge moduli space for reductive algebraic groups, or the intersection theory of some singular Lagrangian cycles. In particular, we study in detail a Dolbeault moduli space which is specialization of the singular irreducible holomorphic symplectic variety of type O'Grady 6. PreliminariesIn this section we introduces preliminary notions and results which will be useful throughout the paper. For further details we refer to [3,29,30,18]. Perverse sheavesAn algebraic variety X is an irreducible separated scheme of finite type over C. Denote by D b c (X) the bounded derived category of Q-constructible complexes on X. Let D : D b c (X) → D b c (X) be the Verdier duality functor. The full subcategoriesX) of the t-structure is the abelian category of perverse sheaves. The truncation functors are denoted p τ ≤k : D b c (X) → p D b ≤k (X), p τ ≥k : D b c (X) → p D b ≥k (X), and the perverse cohomology functors are p H k := p τ ≤k p τ ≥k : D b c (X) → Perv(X).

show abstract

“…By the description in Theorem 1.2 a general variety of type 3 o or 11 o is birational equivalent to a smooth double space branched in a quartic. It is also nonrational [Voi88] (see [CPS19] for special cases).…”

Section: Theorem ([Ale87]mentioning

confidence: 99%