We give a complete description of all smooth projective complex varieties with and .
@article{ASNSP_2012_5_11_2_243_0, author = {Jiang, Zhi}, title = {Varieties with $q(X) = dim(X)$ and $P_2(X)=2$}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {243--258}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {2}, year = {2012}, mrnumber = {3011991}, zbl = {1260.14041}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2012_5_11_2_243_0/} }
TY - JOUR AU - Jiang, Zhi TI - Varieties with $q(X) = dim(X)$ and $P_2(X)=2$ JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 243 EP - 258 VL - 11 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2012_5_11_2_243_0/ LA - en ID - ASNSP_2012_5_11_2_243_0 ER -
%0 Journal Article %A Jiang, Zhi %T Varieties with $q(X) = dim(X)$ and $P_2(X)=2$ %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 243-258 %V 11 %N 2 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2012_5_11_2_243_0/ %G en %F ASNSP_2012_5_11_2_243_0
Jiang, Zhi. Varieties with $q(X) = dim(X)$ and $P_2(X)=2$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 2, pp. 243-258. http://archive.numdam.org/item/ASNSP_2012_5_11_2_243_0/
[1] A. Beauville, “Complex Algebraic Surfaces”, London Math. Soc. Student Text 34, Cambridge University Press, 1992. | MR | Zbl
[2] J. A. Chen and C. D. Hacon, Characterization of Abelian varieties, Invent. Math. 143 (2001), 435–447. | MR | Zbl
[3] J. A. Chen and C. D. Hacon, Pluricanonical maps of varieties of maximal Albanese dimension, Math. Ann. 320 (2001), 367–380. | MR | Zbl
[4] J. A. Chen and C. D. Hacon, Varieties with and , Ann. Sc. Norm. Super. Pisa Cl. Sci. 3 (2004), 399–425. | EuDML | Numdam | MR | Zbl
[5] O. Debarre, On coverings of simple Abelian varieties, Bull. Soc. Math. France 134 (2006), 253–260. | EuDML | Numdam | MR | Zbl
[6] L. Ein and R. Lazarsfeld, Singularities of theta divisors and the birational geometry of irregular varieties, J. Amer. Math. Soc. 10 (1997), 243–258. | MR | Zbl
[7] M. Green and R. Lazarsfeld, Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese and Beauville, Invent. Math. 90 (1987), 389–407. | EuDML | MR | Zbl
[8] M. Green and R. Lazarsfeld, Higher obstructions to deforming cohomology groups of line bundles, J. Amer. Math. Soc. 4 (1991), 87–103. | MR | Zbl
[9] C. D. Hacon, Varieties with and , Math. Nachr. 278 (2005), 409–420. | MR | Zbl
[10] C. D. Hacon, A derived category approach to generic vanishing, J. Reine Angew. Math. 575 (2004), 173–187. | MR | Zbl
[11] C. D. Hacon and R. Pardini, On the birational geometry of varieties of maximal Albanese dimension, J. Reine Angew. Math. 546 (2002), 177–199. | MR | Zbl
[12] Z. Jiang, An effective version of a theorem of Kawamata on the Albanese map, Commun. Contemp. Math. 13 (2011), 509–532. | MR
[13] Y. Kawamata, Characterization of Abelian varieties, Compos. Math. 43 (1981), 253–276. | EuDML | Numdam | MR | Zbl
[14] J. Kollár, Higher direct images of dualizing sheaves I, Ann. of Math. 123 (1986), 11–42. | MR | Zbl
[15] J. Kollár, Higher direct images of dualizing sheaves II, Ann. of Math. 124 (1986), 171–202. | MR | Zbl
[16] R. Lazarsfeld, “Positivity in Algebraic Geometry I & II”, Ergebnisse der Mathematik und ihrer Grenzgebiete 48 and 49, Springer-Verlag, Heidelberg, 2004. | MR | Zbl
[17] S. Mori, Classification of higher-dimensional varieties, Algebraic Geometry, Browdoin 1985, Proc. Sympos. Pure Math. 46 (1987) 269–331. | MR | Zbl
[18] C. Simpson, Subspaces of moduli spaces of rank one local systems, Ann. Sci. École. Norm. Sup. (4) 26 (1993), 361–401. | EuDML | Numdam | MR | Zbl
[19] E. Viehweg, Positivity of direct image sheaves and applications to famillies of higher dimensional manifolds, ICTP-Lecture Notes 6 (2001), 249–284. | MR | Zbl