scholarly journals Brill–Noether theory of curves on Enriques surfaces II: the Clifford index

2014 ◽  
Vol 147 (1-2) ◽  
pp. 193-237 ◽  
Author(s):  
Andreas Leopold Knutsen ◽  
Angelo Felice Lopez
Keyword(s):  
Clifford Index ◽  
Enriques Surfaces

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.

scholarly journals ON ORDINARY ENRIQUES SURFACES IN POSITIVE CHARACTERISTIC

2020 ◽  
pp. 1-14
Author(s):  
ROBERTO LAFACE ◽  
SOFIA TIRABASSI
Keyword(s):  
Positive Characteristic ◽  
Enriques Surfaces

Abstract We give a notion of ordinary Enriques surfaces and their canonical lifts in any positive characteristic, and we prove Torelli-type results for this class of Enriques surfaces.

scholarly journals On the periods of enriques surfaces, I

1977 ◽  
Vol 53 (3) ◽  
pp. 124-127 ◽  
Author(s):  
Eiji Horikawa
Keyword(s):  
Enriques Surfaces

scholarly journals Rank one sheaves over quaternion algebras on Enriques surfaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Fabian Reede
Keyword(s):  
Quaternion Algebra ◽  
Double Cover ◽  
Complex Numbers ◽  
K3 Surface ◽  
Enriques Surface ◽  
Quaternion Algebras ◽  
Enriques Surfaces ◽  
Rank One ◽  
Torsion Free

Abstract Let X be an Enriques surface over the field of complex numbers. We prove that there exists a nontrivial quaternion algebra 𝓐 on X. Then we study the moduli scheme of torsion free 𝓐-modules of rank one. Finally we prove that this moduli scheme is an étale double cover of a Lagrangian subscheme in the corresponding moduli scheme on the associated covering K3 surface.

scholarly journals On automorphisms of Enriques surfaces and their entropy

2018 ◽  
Vol 291 (13) ◽  
pp. 2084-2098
Author(s):  
Yuya Matsumoto ◽  
Hisanori Ohashi ◽  
Sławomir Rams
Keyword(s):  
Enriques Surfaces

scholarly journals A note on stable sheaves on Enriques surfaces

2017 ◽  
Vol 69 (3) ◽  
pp. 369-382 ◽  
Author(s):  
Kōta Yoshioka
Keyword(s):  
Enriques Surfaces ◽  
Stable Sheaves

scholarly journals Logarithmic Enriques surfaces, II

1993 ◽  
Vol 33 (2) ◽  
pp. 357-397 ◽  
Author(s):  
De-Qi Zhang
Keyword(s):  
Enriques Surfaces
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