2014, 21: 126-131. doi: 10.3934/era.2014.21.126

Minkowski bases on algebraic surfaces with rational polyhedral pseudo-effective cone

1. 

Instytut Matematyki, Pedagogical University of Cracow, Podchorążych 2, PL-30-084 Kraków, Poland, Poland

Received  May 2014 Revised  July 2014 Published  August 2014

The purpose of this note is to study the number of elements in Minkowski bases on algebraic surfaces with rational polyhedral pseudo-effective cone.
Citation: Piotr Pokora, Tomasz Szemberg. Minkowski bases on algebraic surfaces with rational polyhedral pseudo-effective cone. Electronic Research Announcements, 2014, 21: 126-131. doi: 10.3934/era.2014.21.126
References:
[1]

Th. Bauer, M. Funke and S. Neumann, Counting Zariski chambers on Del Pezzo surfaces, J. Algebra, 324 (2010), 92-101. doi: 10.1016/j.jalgebra.2010.02.037.

[2]

Th. Bauer, A. Küronya and T. Szemberg, Zariski chambers, volumes, and stable base loci, J. Reine Angew. Math., 576 (2004), 209-233. doi: 10.1515/crll.2004.090.

[3]

K. Kaveh and A. Khovanskii, Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory, Ann. of Math. (2), 176 (2012), 925-978. doi: 10.4007/annals.2012.176.2.5.

[4]

A. Küronya, V. Lozovanu and C. Maclean, Convex bodies appearing as Okounkov bodies of divisors, Adv. Math., 229 (2012), 2622-2639. doi: 10.1016/j.aim.2012.01.013.

[5]

Yu. Manin, Cubic Forms. Algebra, Geometry, Arithmetic, North-Holland Mathematical Library, Vol. 4, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., New York, 1974.

[6]

M. Mustaţă and R. Lazarsfeld, Convex bodies associated to linear series, Ann. Sci. Éc. Norm. Supér. (4), 42 (2009), 783-835.

[7]

P. Łuszcz-Świdecka, On Minkowski Decompositions of Okounkov bodies on a Del Pezzo surface, Ann. Univ. Paedagog. Crac. Stud. Math., 10 (2011), 105-115.

[8]

P. Łuszcz-Świdecka and D. Schmitz, Minkowski decomposition of Okounkov bodies on surfaces, J. Algebra, 414 (2014), 159-174. doi: 10.1016/j.jalgebra.2014.05.024.

[9]

M. Nakamaye, Stable base loci of linear series, Math. Ann., 318 (2000), 837-847. doi: 10.1007/s002080000149.

[10]

P. Pokora, D. Schmitz and S. Urbinati, Minkowski decomposition and generators of the moving cone for toric varieties, arXiv:1310.8505.

show all references

References:
[1]

Th. Bauer, M. Funke and S. Neumann, Counting Zariski chambers on Del Pezzo surfaces, J. Algebra, 324 (2010), 92-101. doi: 10.1016/j.jalgebra.2010.02.037.

[2]

Th. Bauer, A. Küronya and T. Szemberg, Zariski chambers, volumes, and stable base loci, J. Reine Angew. Math., 576 (2004), 209-233. doi: 10.1515/crll.2004.090.

[3]

K. Kaveh and A. Khovanskii, Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory, Ann. of Math. (2), 176 (2012), 925-978. doi: 10.4007/annals.2012.176.2.5.

[4]

A. Küronya, V. Lozovanu and C. Maclean, Convex bodies appearing as Okounkov bodies of divisors, Adv. Math., 229 (2012), 2622-2639. doi: 10.1016/j.aim.2012.01.013.

[5]

Yu. Manin, Cubic Forms. Algebra, Geometry, Arithmetic, North-Holland Mathematical Library, Vol. 4, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., New York, 1974.

[6]

M. Mustaţă and R. Lazarsfeld, Convex bodies associated to linear series, Ann. Sci. Éc. Norm. Supér. (4), 42 (2009), 783-835.

[7]

P. Łuszcz-Świdecka, On Minkowski Decompositions of Okounkov bodies on a Del Pezzo surface, Ann. Univ. Paedagog. Crac. Stud. Math., 10 (2011), 105-115.

[8]

P. Łuszcz-Świdecka and D. Schmitz, Minkowski decomposition of Okounkov bodies on surfaces, J. Algebra, 414 (2014), 159-174. doi: 10.1016/j.jalgebra.2014.05.024.

[9]

M. Nakamaye, Stable base loci of linear series, Math. Ann., 318 (2000), 837-847. doi: 10.1007/s002080000149.

[10]

P. Pokora, D. Schmitz and S. Urbinati, Minkowski decomposition and generators of the moving cone for toric varieties, arXiv:1310.8505.

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