On the Cartwright-Steger surface

Cartwright, Donald; Koziarz, Vincent; Yeung, Sai-Kee

doi:10.48550/arxiv.1412.4137

Cited by 3 publications

(14 citation statements)

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“…The Betti numbers of M 1 are: 1, 2, 5, 2, 1. It is known that the Albanese map of M 1 gives rise to an Albanese fibration with generic fiber of genus 19 [18].…”

Section: Complex Surfaces Of Cartwright Andmentioning

confidence: 99%

“…The covers of Cartwright-Steger surface. Let us recall the following from [18]. In one of our constructions we will be using the curves b(M c ) or b −1 (M c ) in Proposition 2.4 of [18].…”

Section: 3mentioning

confidence: 99%

“…Let us recall the following from [18]. In one of our constructions we will be using the curves b(M c ) or b −1 (M c ) in Proposition 2.4 of [18]. For simplicity, let us consider D = b(M c ).…”

Section: 3mentioning

confidence: 99%

“…Our work here is greatly motivated and influenced by the recent work of Donald Cartwright, Vincent Koziarz, and third author in [18] and the earlier work of Gopal Prasad and the third author in [31,32]. The main purpose of our article is to construct new minimal symplectic 4-manifolds that are interesting with respect to the symplectic geography problem.…”

Section: Introductionmentioning

confidence: 99%

“…We refer the reader to [37] and also [36], where a complete classification of all smooth surfaces of general type with Euler number 3 is given. There are 50 pairs of fake projectives planes as classified in [31,32,18] and one Cartwright-Steger surface to be explained in 2.2.…”

Section: Introductionmentioning

confidence: 99%

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Complex Ball Quotients and New Symplectic 4-manifolds with Nonnegative Signatures

Akhmedov¹,

Sakallı²,

Yeung³

2021

Preprint

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We present the various constructions of new symplectic 4-manifolds with non-negative signatures using the complex surfaces on the BMY line c 2 1 = 9χ h , the Cartwright-Steger surfaces, the quotients of Hirzebruch's certain line-arrangement surfaces, along with the exotic symplectic 4-manifolds constructed in [5,13]. In particular, our constructions yield to (i) an irreducible symplectic and infinitely many non-symplectic 4-manifolds that are homeomorphic but not diffeomorphic to (2n − 1)CP 2 #(2n − 1)CP 2 for each integer n ≥ 9, (ii) the families of simply connected irreducible nonspin symplectic 4-manifolds that have the smallest Euler characteristics among the all known simply connected 4-manifolds with positive signatures and with more than one smooth structure. We also construct a complex surface with positive signature from the Hirzebruch's line-arrangement surfaces, which is a ball quotient.

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“…The Betti numbers of M 1 are: 1, 2, 5, 2, 1. It is known that the Albanese map of M 1 gives rise to an Albanese fibration with generic fiber of genus 19 [18].…”

Section: Complex Surfaces Of Cartwright Andmentioning

confidence: 99%

Section: 3mentioning

confidence: 99%

Section: 3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Complex Ball Quotients and New Symplectic 4-manifolds with Nonnegative Signatures

Akhmedov¹,

Sakallı²,

Yeung³

2021

Preprint

Self Cite

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Kodaira fibrations and beyond: methods for moduli theory

Catanese¹

2017

Jpn. J. Math.

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Abstract. Kodaira fibred surfaces are a remarkable example of projective classifying spaces, and there are still many intriguing open questions concerning them, especially the slope question. The topological characterization of Kodaira fibrations is emblematic of the use of topological methods in the study of moduli spaces of surfaces and higher dimensional complex algebraic varieties, and their compactifications. Our tour through algebraic surfaces and their moduli (with results valid also for higher dimensional varieties) deals with fibrations, questions on monodromy and factorizations in the mapping class group, old and new results on Variation of Hodge Structures, especially a recent answer given (in joint work with Dettweiler) to a long standing question posed by Fujita. In the landscape of our tour, Galois coverings, deformations and rigid manifolds (there are by the way rigid Kodaira fibrations), projective classifying spaces, the action of the absolute Galois group on moduli spaces, stand also in the forefront. These questions lead to interesting algebraic surfaces, for instance remarkable surfaces constructed from VHS, surfaces isogenous to a product with automorphisms acting trivially on cohomology, hypersurfaces in Bagnera-de Franchis varieties, Inoue-type surfaces.

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