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EFFECTIVE CYCLES ON SOME LINEAR BLOWUPS OF PROJECTIVE SPACES

Part of: Projective and enumerative geometry Cycles and subschemes

Published online by Cambridge University Press:  05 December 2019

NORBERT PINTYE  and
ARTIE PRENDERGAST-SMITH Open the ORCID record for ARTIE PRENDERGAST-SMITH [Opens in a new window]
NORBERT PINTYE
Affiliation:
Department of Mathematical Sciences, Loughborough University, LE11 3TU, United Kingdom email [email protected]
ARTIE PRENDERGAST-SMITH
Affiliation:
Department of Mathematical Sciences, Loughborough University, LE11 3TU, United Kingdom email [email protected]
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Abstract

We compute cones of effective cycles on some blowups of projective spaces in general sets of lines.

MSC classification

Primary: 14C25: Algebraic cycles 14N20: Configurations and arrangements of linear subspaces
Type
Article
Information
Nagoya Mathematical Journal , Volume 243 , September 2021 , pp. 243 - 262
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Copyright
© 2019 Foundation Nagoya Mathematical Journal

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References

Coskun, I., Lesieutre, J. and Ottem, J. C., Effective cones of cycles on blowups of projective spaces, Algebra Number Theory 10(9) (2016), 1983–2014.CrossRefGoogle Scholar
Debarre, O., Ein, L., Lazarsfeld, R. and Voisin, C., Pseudoeffective and nef classes on abelian varieties, Compos. Math. 147(6) (2011), 1793–1818.CrossRefGoogle Scholar
Dumitrescu, O., Postinghel, E. and Urbinati, S., Cones of effective divisors on the blown-up P3 in general lines, Rend. Circ. Mat. Palermo (2) 66(2) (2017), 205–216.CrossRefGoogle Scholar
Eisenbud, D. and Harris, J., 3264 And All That, Cambridge University Press, Cambridge, 2016.CrossRefGoogle Scholar
Fulger, M. and Lehmann, B., Zariski decompositions of numerical cycle classes, J. Algebraic Geom. 26(1) (2017), 43–106.10.1090/jag/677CrossRefGoogle Scholar
Fulger, M. and Lehmann, B., Positive cones of dual cycle classes, Algebraic Geom. 4(1) (2017), 1–28.10.14231/AG-2017-001CrossRefGoogle Scholar
Fulton, W., Intersection Theory, 2nd ed. Springer, 1998.CrossRefGoogle Scholar
Grothendieck, A., Éléments de géomtrie algébique. IV. Étude locale des schémas et de morphismes des schémas. III, Publ. Math. Inst. Hautes Études Sci. 28 (1966), Available at http://www.numdam.org/item/PMIHES_1966__28__5_0.Google Scholar
Kleiman, S., The transversality of a general translate, Compos. Math. 28(3) (1974), 287–297.Google Scholar
Li, Q., Pseudo-effective and nef cones on spherical varieties, Math. Z. 280(3–4) (2015), 945–979.10.1007/s00209-015-1457-0CrossRefGoogle Scholar
Macaulay2 computations. Ancillary files available athttps://arxiv.org/abs/1812.08476.Google Scholar
Bruns, W., Ichim, B., Römer, T., Sieg, R. and Söger, C., Normaliz. Algorithms for rational cones and affine monoids. Available at https://www.normaliz.uni-osnabrueck.de.Google Scholar
Ottem, J. C., Ample subvarieties and q-ample divisors, Adv. Math. 229(5) 2868–2887.10.1016/j.aim.2012.02.001CrossRefGoogle Scholar
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