scholarly journals The gonality and the Clifford index of curves on a toric surface

2016 ◽  
Vol 449 ◽  
pp. 660-686 ◽  
Author(s):  
Ryo Kawaguchi
Keyword(s):  
Toric Surface ◽  
Clifford Index

scholarly journals Higher rank Clifford indices of curves on a K3 surface

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Soheyla Feyzbakhsh ◽  
Chunyi Li
Keyword(s):  
Vector Bundles ◽  
Plane Curve ◽  
Smooth Curve ◽  
Line Bundles ◽  
K3 Surface ◽  
Clifford Index ◽  
Smooth Plane ◽  
Higher Rank ◽  
Rank Vector ◽  
Semistable Vector Bundle

AbstractLet (X, H) be a polarized K3 surface with $$\mathrm {Pic}(X) = \mathbb {Z}H$$ Pic ( X ) = Z H , and let $$C\in |H|$$ C ∈ | H | be a smooth curve of genus g. We give an upper bound on the dimension of global sections of a semistable vector bundle on C. This allows us to compute the higher rank Clifford indices of C with high genus. In particular, when $$g\ge r^2\ge 4$$ g ≥ r 2 ≥ 4 , the rank r Clifford index of C can be computed by the restriction of Lazarsfeld–Mukai bundles on X corresponding to line bundles on the curve C. This is a generalization of the result by Green and Lazarsfeld for curves on K3 surfaces to higher rank vector bundles. We also apply the same method to the projective plane and show that the rank r Clifford index of a degree $$d(\ge 5)$$ d ( ≥ 5 ) smooth plane curve is $$d-4$$ d - 4 , which is the same as the Clifford index of the curve.

Tool path optimal design for slow tool servo turning of complex optical surface

2016 ◽  
Vol 231 (5) ◽  
pp. 825-837 ◽  
Author(s):  
Xu Chen ◽  
Min Kang ◽  
Xingsheng Wang ◽  
Muhammad Hassan ◽  
Jun Yang
Keyword(s):  
Optimal Design ◽  
Tool Path ◽  
Tool Path Generation ◽  
Interpolation Error ◽  
Machining Accuracy ◽  
Calculation Error ◽  
Path Generation ◽  
Optical Surface ◽  
Toric Surface ◽  
Slow Tool Servo

In order to increase the machining accuracy of slow tool servo turning of complex optical surface, the optimal design for tool path was studied. A comprehensive tool path generation strategy was proposed to optimize the tool path for machining complex surfaces. A new algorithm was designed for tool nose radius compensation which had less calculation error. Hermite segment interpolation was analyzed based on integrated multi-axes controller, and a new interpolation method referred to as triangle rotary method was put forward and was compared with the area method and three-point method. The machining simulation indicated that the triangle rotary method was significant in error reduction. The interpolation error of toric surface was reduced to 0.0015 µm from 0.06 µm and sinusoidal array surface’s interpolation error decreases to 0.37 µm from 1.5 µm. Finally, a toric surface was machined using optimum tool path generation method to evaluate the proposed tool path generation method.

scholarly journals A metric graph satisfying w41=1$w_4^1 = 1$ that cannot be lifted to a curve satisfying dim⁡ (W41)=1$\dim \;(W_4^1 ) = 1$

2016 ◽  
Vol 14 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Marc Coppens
Keyword(s):  
Linear Systems ◽  
Harmonic Morphism ◽  
Metric Graphs ◽  
Clifford Index ◽  
Special Linear ◽  
Metric Graph ◽  
Index 2

AbstractFor all integers g ≥ 6 we prove the existence of a metric graph G with $w_4^1 = 1$ such that G has Clifford index 2 and there is no tropical modification G′ of G such that there exists a finite harmonic morphism of degree 2 from G′ to a metric graph of genus 1. Those examples show that not all dimension theorems on the space classifying special linear systems for curves have immediate translation to the theory of divisors on metric graphs.

scholarly journals Exceptional sequences of invertible sheaves on rational surfaces

2011 ◽  
Vol 147 (4) ◽  
pp. 1230-1280 ◽  
Author(s):  
Lutz Hille ◽  
Markus Perling
Keyword(s):  
Large Class ◽  
Complete Classification ◽  
Toric Surface ◽  
Structural Result ◽  
Toric Surfaces ◽  
Rational Surfaces ◽  
Exceptional Sequences

AbstractIn this article we consider exceptional sequences of invertible sheaves on smooth complete rational surfaces. We show that to every such sequence one can associate a smooth complete toric surface in a canonical way. We use this structural result to prove various theorems on exceptional and strongly exceptional sequences of invertible sheaves on rational surfaces. We construct full strongly exceptional sequences for a large class of rational surfaces. For the case of toric surfaces we give a complete classification of full strongly exceptional sequences of invertible sheaves.

scholarly journals Counter-examples of high Clifford index to Prym-Torelli

2012 ◽  
Vol 21 (4) ◽  
pp. 769-787 ◽  
Author(s):  
E. Izadi ◽  
H. Lange
Keyword(s):  
Clifford Index

Normal generation and Clifford index on algebraic curves

2007 ◽  
Vol 257 (1) ◽  
pp. 23-31 ◽  
Author(s):  
Youngook Choi ◽  
Seonja Kim ◽  
Young Rock Kim
Keyword(s):  
Algebraic Curves ◽  
Clifford Index

scholarly journals Gonality and Clifford index of curves on K3 surfaces

2003 ◽  
Vol 80 (3) ◽  
pp. 235-238 ◽  
Author(s):  
A. L. Knutsen
Keyword(s):  
K3 Surfaces ◽  
Clifford Index

scholarly journals MINIMALITY AND MUTATION-EQUIVALENCE OF POLYGONS

2017 ◽  
Vol 5 ◽  
Author(s):  
ALEXANDER KASPRZYK ◽  
BENJAMIN NILL ◽  
THOMAS PRINCE
Keyword(s):  
Mirror Symmetry ◽  
Smooth Surface ◽  
Equivalence Classes ◽  
Del Pezzo Surfaces ◽  
Toric Surface ◽  
Del Pezzo

We introduce a concept of minimality for Fano polygons. We show that, up to mutation, there are only finitely many Fano polygons with given singularity content, and give an algorithm to determine representatives for all mutation-equivalence classes of such polygons. This is a key step in a program to classify orbifold del Pezzo surfaces using mirror symmetry. As an application, we classify all Fano polygons such that the corresponding toric surface is qG-deformation-equivalent to either (i) a smooth surface; or (ii) a surface with only singularities of type$1/3(1,1)$.

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