Fake projective planes
From MaRDI portal
Publication:879936
DOI10.1007/s00222-007-0034-5zbMath1253.14034arXivmath/0512115OpenAlexW3101721483MaRDI QIDQ879936
Publication date: 10 May 2007
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0512115
Discrete subgroups of Lie groups (22E40) Class numbers, class groups, discriminants (11R29) Surfaces of general type (14J29)
Related Items
Fake real planes: exotic affine algebraic models of \(\mathbb {R}^{2}\) ⋮ Picard modular groups generated by complex reflections ⋮ On the Cartwright-Steger surface ⋮ On the total curvature and Betti numbers of complex projective manifolds ⋮ Enumeration of the 50 fake projective planes ⋮ Fundamental groups of links of isolated singularities ⋮ Foliations associated to harmonic maps on some complex two ball quotients ⋮ Divisors on surfaces isogenous to a product of mixed type with \(p_g= 0\) ⋮ A surface of maximal canonical degree ⋮ Positivity of the diagonal ⋮ A vanishing result for a Casson-type instanton invariant ⋮ A note on higher extremal metrics ⋮ The densest lattices in \(\mathrm{PGL}_3(\mathbb Q_2)\) ⋮ New canonical triple covers of surfaces ⋮ Asymptotic base loci via Okounkov bodies ⋮ A vanishing theorem on fake projective planes with enough automorphisms ⋮ New tools for classifying Hamiltonian circle actions with isolated fixed points ⋮ Exotic structures arising from fake projective planes ⋮ Discrete subgroups acting transitively on vertices of a Bruhat-Tits building ⋮ Smooth Q$\mathbb {Q}$‐homology planes satisfying the negativity conjecture ⋮ Exceptional collections and the bicanonical map of Keum’s fake projective planes ⋮ Ample subvarieties and \(q\)-ample divisors ⋮ Complex ball quotients and new symplectic \(4\)-manifolds with nonnegative signatures ⋮ Transcendence degree of zero-cycles and the structure of Chow motives ⋮ Cusps of Picard modular surfaces ⋮ Addendum to: ``Exotic structures arising from fake projective planes ⋮ The non-equivariant coherent-constructible correspondence and a conjecture of King ⋮ On compact hyperbolic manifolds of Euler characteristic two ⋮ Nonexistence of arithmetic fake compact Hermitian symmetric spaces of type other than \(A_n\) \((n\leq 4)\) ⋮ Hurwitz ball quotients ⋮ Fake quadrics from irreducible lattices acting on the product of upper half planes ⋮ Examples of Mori dream surfaces of general type with \(p_{g} = 0\) ⋮ Harmonic sections in sphere bundles, normal neighborhoods of reduction loci, and instanton moduli spaces on definite 4-manifolds ⋮ Very ampleness of the bicanonical line bundle on compact complex 2-ball quotients ⋮ Classification and arithmeticity of toroidal compactifications with \(3\overline{c}_2=\overline{c}_1^2=3\) ⋮ Algebraic cycles from a computational point of view ⋮ Addendum to ``Fake projective planes Invent. Math. 168, 321-370 (2007) ⋮ On volumes of complex hyperbolic orbifolds ⋮ Varieties of general type with the same Betti numbers as \(\mathbb{P}^{1}\times \mathbb{P}^{1}\times\cdots\times \mathbb{P}^{1}\) ⋮ Quotients of fake projective planes ⋮ On complex surfaces with definite intersection form ⋮ Volumes of Picard modular surfaces ⋮ NOTES ON AUTOMORPHISMS OF SURFACES OF GENERAL TYPE WITH AND ⋮ Surfaces of general type with geometric genus zero: a survey ⋮ A fake projective plane constructed from an elliptic surface with multiplicities \((2, 4)\) ⋮ Commensurability classes of fake quadrics ⋮ Some (big) irreducible components of the moduli space of minimal surfaces of general type with \(p_{g} = q = 1\) and \(K^{2} = 4\) ⋮ On the syzygies of ample line bundles on fake projective planes ⋮ Geodesic curves on Shimura surfaces ⋮ Residually finite lattices in \(\widetilde{\mathrm{PU}(2,1)}\) and fundamental groups of smooth projective surfaces ⋮ The symplectic isotopy problem for rational cuspidal curves ⋮ Surfaces with canonical map of maximum degree ⋮ Endoscopy and cohomology growth on ⋮ New non-arithmetic complex hyperbolic lattices
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Analytic formulas for the regulator of a number field
- Volumes of S-arithmetic quotients of semi-simple groups. With an appendix by Moshe Jarden and Gopal Prasad
- Finiteness theorems for discrete subgroups of bounded covolume in semi- simple groups
- Vector bundles of rank 2 and linear systems on algebraic surfaces
- Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung
- The strong rigidity theorem for non-Archimedean uniformization
- Computation of the metaplectic kernel
- On the rigidity of certain fundamental groups, arithmeticity of complex hyperbolic lattices, and the ``fake projective planes
- On finite group actions on reductive groups and buildings
- Integrality and arithmeticity of co-compact lattice corresponding to certain complex two-ball quotients of Picard number one
- Canonical models of surfaces of general type
- An Algebraic Surface with K Ample, (K 2 ) = 9, p g = q = 0
- Automorphic Representation of Unitary Groups in Three Variables. (AM-123)
- Lower bounds for discriminants of number fields
- On values of L-functions of totally real algebraic number fields at integers
- The Norm 1 Group of -Adic Division Algebra
- Strong Rigidity of Locally Symmetric Spaces. (AM-78)
- Dirichlet weak uniform distribution of multiplicative functions.
- Some analytic estimates of class numbers and discriminants
