scholarly journals A spectral curve approach to Lawson symmetric CMC surfaces of genus 2

2014 ◽  
Vol 360 (3-4) ◽  
pp. 607-652 ◽  
Author(s):  
Sebastian Heller
Keyword(s):  
Spectral Curve ◽  
Cmc Surfaces ◽  
Genus 2

scholarly journals The spectral curve theory for (k, l)-symmetric CMC surfaces

2015 ◽  
Vol 98 ◽  
pp. 201-213 ◽  
Author(s):  
Lynn Heller ◽  
Sebastian Heller ◽  
Nicholas Schmitt
Keyword(s):  
Spectral Curve ◽  
Cmc Surfaces ◽  
Curve Theory

scholarly journals Uniqueness of Polarization for the Autonomous 4-dimensional Painlevé-type Systems

2020 ◽  
Author(s):  
Akane Nakamura ◽  
Eric Rains
Keyword(s):  
Spectral Curve ◽  
Type Systems ◽  
Abelian Surface ◽  
Integral System ◽  
Genus 2 ◽  
Dimensional Integral

Abstract We prove that for any autonomous 4-dimensional integral system of Painlevé type, the Jacobian of the generic spectral curve has a unique polarization, and thus by Torelli’s theorem cannot be isomorphic as an unpolarized abelian surface to any other Jacobian. This enables us to identify the spectral curve and any irreducible genus 2 component of the boundary of an affine patch of the Liouville torus.

scholarly journals Contact structures and reducible surgeries

2015 ◽  
Vol 152 (1) ◽  
pp. 152-186 ◽  
Author(s):  
Tye Lidman ◽  
Steven Sivek
Keyword(s):  
Contact Structures ◽  
Surgery Theory ◽  
Contact Topology ◽  
Exceptional Surgery ◽  
Genus 2 ◽  
Cabling Conjecture

We apply results from both contact topology and exceptional surgery theory to study when Legendrian surgery on a knot yields a reducible manifold. As an application, we show that a reducible surgery on a non-cabled positive knot of genus$g$must have slope$2g-1$, leading to a proof of the cabling conjecture for positive knots of genus 2. Our techniques also produce bounds on the maximum Thurston–Bennequin numbers of cables.

scholarly journals Spectral curves are transcendental

2021 ◽  
Vol 111 (1) ◽  
Author(s):  
H. W. Braden
Keyword(s):  
Spectral Curve ◽  
Spectral Curves ◽  
Arithmetic Properties ◽  
A Charge

AbstractSome arithmetic properties of spectral curves are discussed: the spectral curve, for example, of a charge $$n\ge 2$$ n ≥ 2 Euclidean BPS monopole is not defined over $$\overline{\mathbb {Q}}$$ Q ¯ if smooth.

scholarly journals Classical spectral curve of the AdS5 × S5 lambda superstring

2020 ◽  
Vol 2020 (5) ◽  
Author(s):  
Timothy J. Hollowood ◽  
J. Luis Miramontes ◽  
Dafydd Price
Keyword(s):  
Spectral Curve

scholarly journals Some Remarks on the Uniformizing Function in Genus 2

2005 ◽  
Vol 115 (1) ◽  
pp. 121-133 ◽  
Author(s):  
Peter Buser ◽  
Robert Silhol
Keyword(s):  
Genus 2
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