Positivity properties for higher (co)dimensional numerical classes on projective varieties

Quick guide to positive cones of numerical classes(PDF) Mihai Fulger,

Positivity in algebraic geometry Robert Lazarsfeld, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., vol. 48, Springer-Verlag, Berlin, 2004

An introduction to volume functions for algebraic cycles(PDF) Brian Lehmann,

The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension Sébastien Boucksom, Jean-Pierre Demailly, Mihai Păun, and Thomas Peternell, J. Algebraic Geom. 22 (2013), no. 2, 201–248.

Pseudo-effective classes and pushforwards Olivier Debarre, Zhi Jiang, and Claire Voisin, Pure and Applied Mathematics Quarterly 9 (2013), no. 4, 643–664.

Positive cones of dual cycle classes Mihai Fulger and Brian Lehmann, 2013, arXiv:1408.5154 .

Morphisms and faces of pseudoeffective cones Mihai Fulger and Brian Lehmann, 2016, arXiv:1601.03314

Kernels of numerical pushforwards Mihai Fulger and Brian Lehmann, 2013, arXiv:1407.6455 .

Positive polynomials for ample vector bundles William Fulton and Robert Lazarsfeld, Ann. of Math. (2) 118 (1983), no. 1, 35–60.

Subvarieties with q-ample normal bundle and q-ample subvarieties Mihai Halic, 2016, arXiv:1511.07524

Ample varieties and $q$-ample divisors John Christian Ottem, Adv. Math. 229 (2012), no. 5, 2868–2887.

On subvarieties with ample normal bundle John Christian Ottem, 2013, arXiv:1309.2263 .

Extremal higher codimension cycles on moduli spaces of curves Dawei Chen and Izzet Coskun, 2014, arXiv:1407.3450 .

Loci of curves with subcanonical points in low genus Dawei Chen and Nicola Tarasca, 2015, arXiv:1501.02235 .

Extremality of Weierstrass points on genus-two curves Dawei Chen and Nicola Tarasca, 2015, arXiv:1510.08061

Effective cones of cycles on blow-ups of projective space Izzet Coskun, and John Lesieutre and John Christian Ottem, 2016, arXiv:1603.04808

Pseudoeffective and nef classes on abelian varieties Olivier Debarre, Lawrence Ein, Robert Lazarsfeld, and Claire Voisin, Compos. Math. 147 (2011), no. 6, 1793–1818.

The cones of effective cycles on projective bundles over curves Mihai Fulger, Math. Z. 269 (2011), no. 1-2, 449–459.

Extremal higher codimension cycles of the space of complete conics César Lozano Huerta, 2015, arXiv:1601.07143 .

The diminished base locus is not always closed John Lesieutre, Compos. Math. 150 (2014), no. 10, 1729–1741.

Nef cycles on some hyperkahler fourfolds John Ottem, 2015, arXiv:1505.01477 .

On the cone of effective 2-cycles on $\overline{M}_{0,7}$ Luca Schaffler, 2015, arXiv:1501.01736 .

Coniveau 2 complete intersections and effective cones Claire Voisin, Geom. Funct. Anal. 19 (2010), no. 5, 1494–1513.

Effective divisors on Bott-Samuelson varieties David Anderson, 2015, arXiv:1501.00034

A tropical approach to the strongly positive Hodge conjecture Farhad Babaee and June Huh, 2015, arXiv:1502.00299 .

Correspondences between projective planes June Huh, 2014, arXiv:1303.4113 .

Pseudo-effective and nef cones on spherical varieties Qifeng Li, Math. Z. 280 (2015), no. 3-4, 945–979.

Zariski decompositions of numerical cycle classes Mihai Fulger and Brian Lehmann, 2013, arXiv:1310.0538, to appear in J. of Alg. Geom.

Volume-type functions for numerical classes Brian Lehmann, 2015, arXiv:1601.03276 .

Convexity and Zariski decomposition structure(PDF) Brian Lehmann and Jian Xiao, 2016

Positivity functions for curves on algebraic varieties(PDF) Brian Lehmann and Jian Xiao, 2016

Characterizing volume via cone duality Jian Xiao, 2015, arXiv:1502.06450 .

Positivity and excess intersection William Fulton and Robert Lazarsfeld, Enumerative geometry and classical algebraic geometry (Nice, 1981), Progr. Math., 24, Birkhäuser, Boston, Mass., 1982, 97–105.

$p$-ample bundles and their Chern classes David Gieseker, Nagoya Math. J., 43, 1971, 91–116.

Ample subvarieties of algebraic varieties Robin Hartshorne, Lecture Notes in Mathematics, Vol. 156, Springer-Verlag, Berlin-New York, 1970.

The transversality of a general translate Steven L. Kleiman, Compos. Math., 28, no.3, 1974, 287–297.

Submanifolds with ample normal bundles and a conjecture of Hartshorne Thomas Peternell, Interactions of classical and numerical algebraic geometry, Contemp. Math., 496, Amer. Math. Soc., Providence, RI, 2009, 317–330.