[1]

V. Alexeev and A. Brunyate,
Extending Torelli map to toroidal compactifications of Siegel space,
Invent. Math. 188 (2011), no. 1, 175â€“196.
WebÂ ofÂ ScienceGoogleÂ Scholar

[2]

A. Ash, D. Mumford, M. Rapoport and Y. Tai,
Smooth compactification of locally symmetric varieties, 2nd ed.,
Cambridge Math. Lib.,
Cambridge University Press, Cambridge 2010.
GoogleÂ Scholar

[3]

E. Baranovskii and V. Grishukhin,
Non-rigidity degree of a lattice and rigid lattices,
European J. Combin. 22 (2001), no. 7, 921â€“935.
CrossrefGoogleÂ Scholar

[4]

G. Barthel, J.-P. Brasselet, K.-H. Fieseler, O. Gabber and L. Kaup,
RelĂ¨vement de cycles algĂ©briques et homomorphismes associĂ©s en homologie dâ€™intersection,
Ann. of Math. (2) 141 (1995), no. 1, 147â€“179.
CrossrefGoogleÂ Scholar

[5]

A. Borel,
Stable real cohomology of arithmetic groups,
Ann. Sci. Ă‰c. Norm. SupĂ©r. (4) 7 (1974), 235â€“272.
CrossrefGoogleÂ Scholar

[6]

A. Borel,
Stable real cohomology of arithmetic groups II,
Manifolds and groups. Papers in honor of Yozo Matsushima,
Progr. Math. 14,
BirkhĂ¤user, Basel (1981), 21â€“55.
GoogleÂ Scholar

[7]

R. Charney and R. Lee,
Cohomology of the Satake compactification,
Topology 22 (1983), no. 4, 389â€“423.
WebÂ ofÂ ScienceCrossrefGoogleÂ Scholar

[8]

J. Chen and E. Looijenga,
On the stable cohomology of the Satake compactification and its mixed Hodge structure,
in preparation.

[9]

D. Cox, J. Little and H. Schenck,
Toric varieties,
Grad. Stud. Math. 124,
American Mathematical Society, Providence 2011.
GoogleÂ Scholar

[10]

P. Deligne,
ThĂ©orĂ¨me de Lefschetz et critĂ¨res de dĂ©gĂ©nĂ©rescence de suites spectrales,
Publ. Math. Inst. Hautes Ă‰tudes Sci. 35 (1968), 259â€“278.
GoogleÂ Scholar

[11]

C. Deninger and J. Murre,
Motivic decomposition of abelian schemes and the Fourier transform,
J. reine angew. Math. 422 (1991), 201â€“219.
GoogleÂ Scholar

[12]

M. Deza and V. Grishukhin,
Nonrigidity degree of root lattices and their duals,
Geom. Dedicata 104 (2004), 15â€“24.
CrossrefGoogleÂ Scholar

[13]

A. Durfee,
Intersection homology Betti numbers,
Proc. Amer. Math. Soc. 123 (1995), no. 4, 989â€“993.
CrossrefGoogleÂ Scholar

[14]

M. Dutour SikiriÄ‡, K. Hulek and A. SchĂĽrmann,
Smoothness and singularities of the perfect form compactification of ${\mathcal{\u0111\u0165\u2019\u015b}}_{g}$,
Algebraic Geom. 2 (2015), no. 5, 642â€“653.
GoogleÂ Scholar

[15]

D. Eisenbud,
Commutative algebra. With a view toward algebraic geometry,
Grad. Texts in Math. 150,
Springer, New York 1995.
GoogleÂ Scholar

[16]

P. Elbaz-Vincent, H. Gangl and C. SoulĂ©,
Perfect forms, *K*-theory and the cohomology of modular groups,
Adv. Math. 245 (2013), 587â€“624.
CrossrefWebÂ ofÂ ScienceGoogleÂ Scholar

[17]

R. Erdahl and S. Ryshkov,
The empty sphere. II,
Canad. J. Math. 40 (1988), no. 5, 1058â€“1073.
CrossrefGoogleÂ Scholar

[18]

R. Erdahl and S. Ryshkov,
On lattice dicing,
European J. Combin. 15 (1994), no. 5, 459â€“481.
CrossrefGoogleÂ Scholar

[19]

G. Faltings and C.-L. Chai,
Degeneration of abelian varieties,
Ergeb. Math. Grenzgeb. (3) 22,
Springer, Berlin 1990.
GoogleÂ Scholar

[20]

W. Fulton,
Intersection theory, 2nd ed.,
Ergeb. Math. Grenzgeb. (3) 2,
Springer, Berlin 1998.
GoogleÂ Scholar

[21]

W. Fulton and J. Harris,
Representation theory,
Grad. Texts in Math. 129,
Springer, New York 1991.
GoogleÂ Scholar

[22]

G. van der Geer,
The Chow ring of the moduli space of abelian threefolds,
J. Algebraic Geom. 7 (1998), no. 4, 753â€“770.
WebÂ ofÂ ScienceGoogleÂ Scholar

[23]

J. Giansiracusa and G. Sankaran,
personal communication, 2013.

[24]

S. Grushevsky,
Geometry of ${\mathcal{\u0111\u0165\u2019\u015b}}_{g}$ and its compactifications,
Algebraic geometryâ€”Seattle 2005. Part 1,
Proc. Sympos. Pure Math. 80,
American Mathematical Society, Providence (2009), 193â€“234.
GoogleÂ Scholar

[25]

S. Grushevsky and K. Hulek,
Principally polarized semiabelic varieties of torus rank up to 3, and the Andreottiâ€“Mayer loci,
Pure Appl. Math. Q. 7 (2011), 1309â€“1360.
CrossrefGoogleÂ Scholar

[26]

S. Grushevsky and K. Hulek,
The class of the locus of intermediate Jacobians of cubic threefolds,
Invent. Math. 190 (2012), no. 1, 119â€“168.
WebÂ ofÂ ScienceCrossrefGoogleÂ Scholar

[27]

S. Grushevsky and K. Hulek,
Geometry of theta divisorsâ€”A survey,
A celebration of algebraic geometry,
Clay Math. Proc. 18,
American Mathematical Society, Providence (2013), 361â€“390.
GoogleÂ Scholar

[28]

R. Hain,
Infinitesimal presentations of the Torelli groups,
J. Amer. Math. Soc. 10 (1997), no. 3, 597â€“651.
CrossrefGoogleÂ Scholar

[29]

R. Hain,
The rational cohomology ring of the moduli space of abelian 3-folds,
Math. Res. Lett. 9 (2002), no. 4, 473â€“491.
CrossrefGoogleÂ Scholar

[30]

R. Hain,
Normal functions and the geometry of moduli spaces of curves,
Handbook of moduli. Vol. I,
International Press, Somerville (2013), 527â€“578.
GoogleÂ Scholar

[31]

J.â€‰L. Harer,
Stability of the homology of the mapping class groups of orientable surfaces,
Ann. of Math. (2) 121 (1985), no. 2, 215â€“249.
CrossrefGoogleÂ Scholar

[32]

A. Hatcher,
Algebraic topology,
Cambridge University Press, Cambridge 2002.
GoogleÂ Scholar

[33]

K. Hulek and O. Tommasi,
Cohomology of the toroidal compactification of ${\mathcal{\u0111\u0165\u2019\u015b}}_{3}$,
Vector bundles and complex geometry,
Contemp. Math. 522,
American Mathematical Society, Providence (2010), 89â€“103.
GoogleÂ Scholar

[34]

K. Hulek and O. Tommasi,
Cohomology of the second Voronoi compactification of ${\mathcal{\u0111\u0165\u2019\u015b}}_{4}$,
Doc. Math. 17 (2012), 195â€“244.
GoogleÂ Scholar

[35]

E. Looijenga and V. Lunts,
A Lie algebra attached to a projective variety,
Invent. Math. 129 (1997), no. 2, 361â€“412.
CrossrefGoogleÂ Scholar

[36]

I. Madsen and M. Weiss,
The stable moduli space of Riemann surfaces: Mumfordâ€™s conjecture,
Ann. of Math. (2) 165 (2007), no. 3, 843â€“941.
WebÂ ofÂ ScienceCrossrefGoogleÂ Scholar

[37]

M. Melo and F. Viviani,
Comparing perfect and 2nd Voronoi decompositions: The matroidal locus,
Math. Ann. 354 (2012), no. 4, 1521â€“1554.
CrossrefWebÂ ofÂ ScienceGoogleÂ Scholar

[38]

B. Moonen,
On the Chow motive of an abelian scheme with non-trivial endomorphisms,
J. reine angew. Math. (2014), 10.1515/crelle-2013-0115.
WebÂ ofÂ ScienceGoogleÂ Scholar

[39]

D. Mumford,
Hirzebruchâ€™s proportionality theorem in the noncompact case,
Invent. Math. 42 (1977), 239â€“272.
CrossrefGoogleÂ Scholar

[40]

D. Mumford,
On the Kodaira dimension of the Siegel modular variety,
Algebraic geometryâ€”Open problems (Ravello 1982),
Lecture Notes in Math. 997,
Springer, Berlin (1983), 348â€“375.
GoogleÂ Scholar

[41]

Y. Namikawa,
Toroidal compactification of Siegel spaces,
Lecture Notes in Math. 812,
Springer, Berlin 1980.
GoogleÂ Scholar

[42]

C.â€‰A.â€‰M. Peters and J.â€‰H.â€‰M. Steenbrink,
Mixed Hodge structures,
Ergeb. Math. Grenzgeb. (3) 52,
Springer, Berlin 2008.
GoogleÂ Scholar

[43]

N. Shepherd-Barron,
Perfect forms and the moduli space of abelian varieties,
Invent. Math. 163 (2006), no. 1, 25â€“45.
CrossrefGoogleÂ Scholar

[44]

G. Thompson,
Skew invariant theory of symplectic groups, pluri-Hodge groups and 3-manifold invariants,
Int. Math. Res. Not. IMRN 2007 (2007), no. 15, Article ID rnm048.
GoogleÂ Scholar

[45]

F. Vallentin,
Sphere coverings, lattices, and tilings (in low dimensions),
PhD thesis, Center for Mathematical Sciences, Munich University of Technology, Munich 2003.
GoogleÂ Scholar

[46]

C. Voisin,
Chow rings, decomposition of the diagonal and the topology of families,
Ann. of Math. Stud. 187,
Princeton University Press, Princeton 2014.
GoogleÂ Scholar

[47]

G. Voronoi,
Nouvelles applications des paramĂ¨tres continus Ă la thĂ©orie des formes quadratiques. Premier mĂ©moire. Sur quelques propriĂ©tĂ©s des formes quadratiques positives parfaites,
J. reine angew. Math. 134 (1908), 79â€“178.
GoogleÂ Scholar

[48]

G. Voronoi,
Nouvelles applications des paramĂ¨tres continus Ă la thĂ©orie des formes quadratiques. DeuxiĂ¨me mĂ©moire. Recherches sur les parallĂ©loĂ¨dres primitifs,
J. reine angew. Math. 134 (1908), 198â€“287.
GoogleÂ Scholar

[49]

G. Voronoi,
Nouvelles applications des paramĂ¨tres continus Ă la thĂ©orie des formes quadratiques. DeuxiĂ¨me mĂ©moire. Seconde partie: domaines de formes quadratiques correspondants aux diffĂ©rents types deparallĂ©loĂ¨dres primitifs,
J. reine angew. Math. 136 (1909), 67â€“178.
GoogleÂ Scholar

## CommentsÂ (0)

General note:By using the comment function on degruyter.com you agree to our Privacy Statement. A respectful treatment of one another is important to us. Therefore we would like to draw your attention to our House Rules.