scholarly journals Note on spun normal surfaces in 1-efficient ideal triangulations

2015 ◽  
Vol 91 (8) ◽  
pp. 118-122
Author(s):  
Ensil Kang ◽  
Joachim Hyam Rubinstein
Keyword(s):  
Normal Surfaces ◽  
Ideal Triangulations

scholarly journals Normal surfaces in non-compact 3-manifolds

2005 ◽  
Vol 78 (3) ◽  
pp. 305-321 ◽  
Author(s):  
Ensil Kang
Keyword(s):  
Finite Number ◽  
Infinite Number ◽  
Boundary Component ◽  
Unique Feature ◽  
Admissible Solution ◽  
Compact Surface ◽  
Normal Surface ◽  
Ideal Triangulation ◽  
Normal Surfaces ◽  
Ideal Triangulations

AbstractWe extend the normal surface Q-theory to non-compact 3-manifolds with respect to ideal triangulations. An ideal triangulation of a 3-manifold often has a small number of tetrahedra resulting in a system of Q-matching equations with a small number of variables. A unique feature of our approach is that a compact surface F with boundary properly embedded in a non-compact 3-manifold M with an ideal triangulation with torus cusps can be represented by a normal surface in M as follows. A half-open annulus made up of an infinite number of triangular disks is attached to each boundary component of F. The resulting surface , when normalized, will contain only a finite number of Q-disks and thus correspond to an admissible solution to the system of Q-matching equations. The correspondence is bijective.

scholarly journals A METHOD TO FIND IDEAL POINTS FROM IDEAL TRIANGULATIONS

2010 ◽  
Vol 19 (04) ◽  
pp. 509-524
Author(s):  
YUICHI KABAYA
Keyword(s):  
Linear Algebra ◽  
Character Variety ◽  
Ideal Triangulations ◽  
Ideal Points

We give a method to find ideal points of the character variety of a 3-manifold with toral boundary. This can be easily carried out by using linear algebra.

ℤ3-actions on Horikawa surfaces

2021 ◽  
pp. 2150097
Author(s):  
Vicente Lorenzo
Keyword(s):  
Moduli Space ◽  
General Type ◽  
Admissible Pair ◽  
Algebraic Surfaces ◽  
The Other ◽  
Connected Components ◽  
Surfaces Of General Type ◽  
Canonical Models ◽  
Normal Surfaces ◽  
Stable Surfaces

Minimal algebraic surfaces of general type [Formula: see text] such that [Formula: see text] are called Horikawa surfaces. In this note, [Formula: see text]-actions on Horikawa surfaces are studied. The main result states that given an admissible pair [Formula: see text] such that [Formula: see text], all the connected components of Gieseker’s moduli space [Formula: see text] contain surfaces admitting a [Formula: see text]-action. On the other hand, the examples considered allow us to produce normal stable surfaces that do not admit a [Formula: see text]-Gorenstein smoothing. This is illustrated by constructing non-smoothable normal surfaces in the KSBA-compactification [Formula: see text] of Gieseker’s moduli space [Formula: see text] for every admissible pair [Formula: see text] such that [Formula: see text]. Furthermore, the surfaces constructed belong to connected components of [Formula: see text] without canonical models.

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