scholarly journals k—Very Ample Line Bundles on Del Pezzo Surfaces

1996 ◽  
Vol 179 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Sandra di Rocco

Author(s):  
Fabio Bernasconi ◽  
Hiromu Tanaka

We establish two results on three-dimensional del Pezzo fibrations in positive characteristic. First, we give an explicit bound for torsion index of relatively torsion line bundles. Second, we show the existence of purely inseparable sections with explicit bounded degree. To prove these results, we study log del Pezzo surfaces defined over imperfect fields.



2013 ◽  
Vol 149 (11) ◽  
pp. 1839-1855 ◽  
Author(s):  
Raf Bocklandt

AbstractIn their paper [Exceptional sequences of invertible sheaves on rational surfaces, Compositio Math. 147 (2011), 1230–1280], Hille and Perling associate to every cyclic full strongly exceptional sequence of line bundles on a toric weak del Pezzo surface a toric system, which defines a new toric surface. We interpret this construction as an instance of mirror symmetry and extend it to a duality on the set of toric weak del Pezzo surfaces equipped with a cyclic full strongly exceptional sequence.





2018 ◽  
Vol 2020 (10) ◽  
pp. 3130-3152
Author(s):  
Drew Johnson

Abstract We show how the “finite Quot scheme method” applied to Le Potier’s strange duality on del Pezzo surfaces leads to conjectures (valid for all smooth complex projective surfaces) relating two sets of universal power series on Hilbert schemes of points on surfaces: those for top Chern classes of tautological sheaves and those for Euler characteristics of line bundles. We have verified these predictions computationally for low order. We then give an analysis of these conjectures in small ranks. We also give a combinatorial proof of a formula predicted by our conjectures: the top Chern class of the tautological sheaf on $S^{[n]}$ associated to the structure sheaf of a point is equal to $(-1)^n$ times the nth Catalan number.



2016 ◽  
Vol 16 (4) ◽  
pp. 691-709 ◽  
Author(s):  
Alexey Elagin ◽  
Valery Lunts


2021 ◽  
Vol 8 (1) ◽  
pp. 223-229
Author(s):  
Callum R. Brodie ◽  
Andrei Constantin ◽  
Rehan Deen ◽  
Andre Lukas

Abstract We show that the zeroth cohomology of effective line bundles on del Pezzo and Hirzebruch surfaces can always be computed in terms of a topological index.





2009 ◽  
Vol 3 (7) ◽  
pp. 729-761 ◽  
Author(s):  
Damiano Testa ◽  
Anthony Várilly-Alvarado ◽  
Mauricio Velasco


2016 ◽  
Vol 300 ◽  
pp. 156-189 ◽  
Author(s):  
Qingchun Ren ◽  
Kristin Shaw ◽  
Bernd Sturmfels
Keyword(s):  


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