scholarly journals Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone

2018 ◽  
Vol 20 (3) ◽  
pp. 407-436 ◽  
Author(s):  
Giovanni Bellettini ◽  
Maurizio Paolini ◽  
Franco Pasquarelli
Keyword(s):  
Connected Surface ◽  
Simply Connected

scholarly journals A simply connected surface of general type withpg= 0 andK2= 4

2009 ◽  
Vol 13 (3) ◽  
pp. 1483-1494 ◽  
Author(s):  
Heesang Park ◽  
Jongil Park ◽  
Dongsoo Shin
Keyword(s):  
General Type ◽  
Connected Surface ◽  
Surface Of General Type ◽  
Simply Connected

scholarly journals Characterisation theorems for compact hypercomplex manifolds

1987 ◽  
Vol 43 (2) ◽  
pp. 231-245
Author(s):  
S. Nag ◽  
J. A. Hillman ◽  
B. Datta
Keyword(s):  
Projective Space ◽  
Finite Number ◽  
Riemann Surfaces ◽  
Conformal Structure ◽  
Dimensional Manifold ◽  
Real Projective Space ◽  
Geometric Methods ◽  
Connected Surface ◽  
Compact Riemann Surfaces ◽  
Simply Connected

AbstractWe have defined and studied some pseudogroups of local diffeomorphisms which generalise the complex analytic pseudogroups. A 4-dimensional (or 8-dimensional) manifold modelled on these ‘Further pseudogroups’ turns out to be a quaternionic (respectively octonionic) manifold.We characterise compact Further manifolds as being products of compact Riemann surfaces with appropriate dimensional spheres. It then transpires that a connected compact quaternionic (H) (respectively O) manifold X, minus a finite number of circles (its ‘real set’), is the orientation double covering of the product Y × P2, (respectively Y×P6), where Y is a connected surface equipped with a canonical conformal structure and Pn is n-dimensonal real projective space.A corollary is that the only simply-connected compact manifolds which can allow H (respectively O) structure are S4 and S2 × S2 (respectively S8 and S2×S6).Previous authors, for example Marchiafava and Salamon, have studied very closely-related classes of manifolds by differential geometric methods. Our techniques in this paper are function theoretic and topological.

scholarly journals The Gromov–Witten invariants of the Hilbert schemes of points on surfaces with pg > 0

2015 ◽  
Vol 26 (01) ◽  
pp. 1550009 ◽  
Author(s):  
Jianxun Hu ◽  
Wei-Ping Li ◽  
Zhenbo Qin
Keyword(s):  
Moduli Space ◽  
Zero Divisor ◽  
Homology Class ◽  
Projective Surface ◽  
Hilbert Schemes ◽  
Geometric Genus ◽  
Holomorphic Differential ◽  
Witten Theory ◽  
Connected Surface ◽  
Simply Connected

In this paper, we study the Gromov–Witten theory of the Hilbert schemes X[n] of points on a smooth projective surface X with positive geometric genus pg. For fixed distinct points x1, …, xn-1 ∈ X, let βn be the homology class of the curve {ξ + x2 + ⋯ + xn-1 ∈ X[n] | Supp (ξ) = {x1}}, and let βKX be the homology class of {x + x1 + ⋯ + xn-1 ∈ X[n] | x ∈ KX}. Using cosection localization technique due to Y. Kiem and J. Li, we prove that if X is a simply connected surface admitting a holomorphic differential two-form with irreducible zero divisor, then all the Gromov–Witten invariants of X[n] defined via the moduli space [Formula: see text] of stable maps vanish except possibly when β is a linear combination of βn and βKX. When n = 2, the exceptional cases can be further reduced to the Gromov–Witten invariants: [Formula: see text] with [Formula: see text] and d ≤ 3, and [Formula: see text] with d ≥ 1. When [Formula: see text], we show that [Formula: see text] which is consistent with a well-known formula of C. Taubes. In addition, for an arbitrary surface X and d ≥ 1, we verify that [Formula: see text].

scholarly journals Erratum to the article A simply connected surface of general type withpg= 0 andK2= 3

2011 ◽  
Vol 15 (1) ◽  
pp. 499-500 ◽  
Author(s):  
Heesang Park ◽  
Jongil Park ◽  
Dongsoo Shin
Keyword(s):  
General Type ◽  
Connected Surface ◽  
Surface Of General Type ◽  
Simply Connected

scholarly journals A simply connected surface of general type withpg= 0 andK2= 3

2009 ◽  
Vol 13 (2) ◽  
pp. 743-767 ◽  
Author(s):  
Heesang Park ◽  
Jongil Park ◽  
Dongsoo Shin
Keyword(s):  
General Type ◽  
Connected Surface ◽  
Surface Of General Type ◽  
Simply Connected
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