scholarly journals Topological Formulae for the Zeroth Cohomology of Line Bundles on del Pezzo and Hirzebruch Surfaces

2021 ◽  
Vol 8 (1) ◽  
pp. 223-229
Author(s):  
Callum R. Brodie ◽  
Andrei Constantin ◽  
Rehan Deen ◽  
Andre Lukas
Keyword(s):  
Topological Index ◽  
Line Bundles ◽  
Hirzebruch Surfaces ◽  
Del Pezzo

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.

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

1996 ◽  
Vol 179 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Sandra di Rocco
Keyword(s):  
Line Bundles ◽  
Del Pezzo Surfaces ◽  
Del Pezzo

scholarly journals ON DEL PEZZO FIBRATIONS IN POSITIVE CHARACTERISTIC

2020 ◽  
pp. 1-43
Author(s):  
Fabio Bernasconi ◽  
Hiromu Tanaka
Keyword(s):  
Positive Characteristic ◽  
Three Dimensional ◽  
Line Bundles ◽  
Del Pezzo Surfaces ◽  
Bounded Degree ◽  
Explicit Bound ◽  
Del Pezzo ◽  
Log Del Pezzo Surfaces

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.

scholarly journals Toric systems and mirror symmetry

2013 ◽  
Vol 149 (11) ◽  
pp. 1839-1855 ◽  
Author(s):  
Raf Bocklandt
Keyword(s):  
Mirror Symmetry ◽  
Line Bundles ◽  
Del Pezzo Surfaces ◽  
Toric Surface ◽  
Exceptional Sequence ◽  
Del Pezzo Surface ◽  
Rational Surfaces ◽  
Exceptional Sequences ◽  
Del Pezzo ◽  
Compositio Math

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.

scholarly journals Line bundles and curves on a del Pezzo order

2013 ◽  
Vol 387 ◽  
pp. 117-143
Author(s):  
Boris Lerner
Keyword(s):  
Line Bundles ◽  
Del Pezzo

scholarly journals Blown-Up Hirzebruch Surfaces and Special Divisor Classes

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 867
Author(s):  
Jae-Hyouk Lee ◽  
YongJoo Shin
Keyword(s):  
Complex Numbers ◽  
Del Pezzo Surfaces ◽  
Positivity Condition ◽  
Fundamental Properties ◽  
Special Divisor ◽  
Hirzebruch Surfaces ◽  
Del Pezzo

We work on special divisor classes on blow-ups F p , r of Hirzebruch surfaces over the field of complex numbers, and extend fundamental properties of special divisor classes on del Pezzo surfaces parallel to analogous ones on surfaces F p , r . We also consider special divisor classes on surfaces F p , r with respect to monoidal transformations and explain the tie-ups among them contrast to the special divisor classes on del Pezzo surfaces. In particular, the fundamental properties of quartic rational divisor classes on surfaces F p , r are studied, and we obtain interwinded relationships among rulings, exceptional systems and quartic rational divisor classes along with monoidal transformations. We also obtain the effectiveness for the rational divisor classes on F p , r with positivity condition.

scholarly journals On exceptional collections of line bundles and mirror symmetry for toric Del-Pezzo surfaces

2017 ◽  
Vol 58 (3) ◽  
pp. 031704 ◽  
Author(s):  
Yochay Jerby
Keyword(s):  
Mirror Symmetry ◽  
Line Bundles ◽  
Del Pezzo Surfaces ◽  
Del Pezzo

scholarly journals Universal Series for Hilbert Schemes and Strange Duality

2018 ◽  
Vol 2020 (10) ◽  
pp. 3130-3152
Author(s):  
Drew Johnson
Keyword(s):  
Combinatorial Proof ◽  
Line Bundles ◽  
Del Pezzo Surfaces ◽  
Hilbert Schemes ◽  
Euler Characteristics ◽  
Quot Scheme ◽  
Del Pezzo ◽  
Complex Projective ◽  
Strange Duality ◽  
Projective Surfaces

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.

scholarly journals On Full Exceptional Collections of Line Bundles on del Pezzo Surfaces

2016 ◽  
Vol 16 (4) ◽  
pp. 691-709 ◽  
Author(s):  
Alexey Elagin ◽  
Valery Lunts
Keyword(s):  
Line Bundles ◽  
Del Pezzo Surfaces ◽  
Del Pezzo

Condensation of CFC-11 and HCFC-123 in In-Line Bundles of Horizontal Finned Tubes: Effect of Fin Geometry

1994 ◽  
Vol 1 (2) ◽  
pp. 197-209 ◽  
Author(s):  
Hiroshi Honda ◽  
Hiroshi Takamatsu ◽  
Kyoohee Kim
Keyword(s):  
Line Bundles ◽  
Finned Tubes ◽  
Hcfc 123
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