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On degenerations of moduli of Hitchin pairs
Characteristic classes of singular toric varieties
1. | Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, United States |
2. | Mathematische Institut, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany |
References:
[1] |
P. Aluffi, Classes de Chern pour variétés singulières, revisitées, C. R. Math. Acad. Sci. Paris, 342 (2006), 405-410.
doi: 10.1016/j.crma.2006.01.002. |
[2] |
A. Barvinok and J. E. Pommersheim, An algorithmic theory of lattice points in polyhedra, in New Perspectives in Algebraic Combinatorics (Berkeley, CA, 1996-97), Math. Sci. Res. Inst. Publ., 38, Cambridge Univ. Press, Cambridge, 1999, 91-147. |
[3] |
P. Baum, W. Fulton and R. MacPherson, Riemann-Roch for singular varieties, Inst. Hautes Études Sci. Publ. Math., 45 (1975), 101-145. |
[4] |
G. Barthel, J.-P. Brasselet and K.-H. Fieseler, Classes de Chern des variétés toriques singulières, C. R. Acad. Sci. Paris Sér. I Math., 315 (1992), 187-192. |
[5] |
J.-P. Brasselet, J. Schürmann and S. Yokura, Hirzebruch classes and motivic Chern classes of singular spaces, J. Topol. Anal., 2 (2010), 1-55.
doi: 10.1142/S1793525310000239. |
[6] |
M. Brion and M. Vergne, An equivariant Riemann-Roch theorem for complete, simplicial toric varieties, J. Reine Angew. Math., 482 (1997), 67-92. |
[7] |
S. E. Cappell, L. Maxim, J. Schürmann and J. L. Shaneson, Equivariant characteristic classes of complex algebraic varieties, Comm. Pure Appl. Math., 65 (2012), 1722-1769.
doi: 10.1002/cpa.21427. |
[8] |
S. E. Cappell and J. L. Shaneson, Genera of algebraic varieties and counting of lattice points, Bull. Amer. Math. Soc. (N.S.), 30 (1994), 62-69.
doi: 10.1090/S0273-0979-1994-00436-7. |
[9] |
S. E. Cappell and J. L. Shaneson, Euler-MacLaurin expansions for lattices above dimension one, C. R. Acad. Sci. Paris Sér. I Math., 321 (1995), 885-890. |
[10] |
D. Cox, The homogeneous coordinate ring of a toric variety, J. Alg. Geom., 4 (1995), 17-50. |
[11] |
D. Cox, J. Little and H. Schenck, Toric Varieties, Graduate Studies in Mathematics, 124, American Mathematical Society, Providence, RI, 2011. |
[12] |
V. I. Danilov, The geometry of toric varieties, Russian Math. Surveys, 33 (1978), 97-154.
doi: 10.1070/RM1978v033n02ABEH002305. |
[13] |
D. Edidin and W. Graham, Riemann-Roch for quotients and Todd classes of simplicial toric varieties, Comm. Algebra, 31 (2003), 3735-3752.
doi: 10.1081/AGB-120022440. |
[14] |
K. E. Feldman, Miraculous cancellation and Pick's theorem, in Toric Topology, Contemp. Math., 460, Amer. Math. Soc., Providence, RI, 2008, 71-86.
doi: 10.1090/conm/460/09011. |
[15] |
W. Fulton, Introduction to Toric Varieties, Annals of Mathematics Studies, 131, Princeton University Press, Princeton, NJ, 1993. |
[16] |
St. Garoufalidis and J. E. Pommersheim, Values of zeta functions at negative integers, Dedekind sums and toric geometry, J. Amer. Math. Soc., 14 (2001), 1-23.
doi: 10.1090/S0894-0347-00-00352-0. |
[17] |
I. Gessel, Generating functions and generalized Dedekind sums, Electron. J. Combin., 4 (1997), 17 pp. |
[18] |
M.-N. Ishida, Torus embeddings and de Rham complexes, in Commutative Algebra and Combinatorics (Kyoto, 1985), Adv. Stud. Pure Math., 11, North-Holland, Amsterdam, (1987), 111-145. |
[19] |
E. Materov, The Bott formula for toric varieties, Mosc. Math. J., 2 (2002), 161-182, 200. |
[20] |
L. Maxim and J. Schürmann, Characteristic classes of singular toric varieties, arXiv:1303.4454. |
[21] |
B. Moonen, Das Lefschetz-Riemann-Roch-Theorem für Singuläre Varietäten, Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn. Bonner Mathematische Schriften, 106, Universität Bonn, Mathematisches Institut, Bonn, 1978. |
[22] |
N. C. Leung and V. Reiner, The signature of a toric variety, Duke Math. J., 111 (2002), 253-286.
doi: 10.1215/S0012-7094-02-11123-5. |
[23] |
T. Oda, Convex Bodies and Algebraic Geometry. An Introduction to the Theory of Toric Varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 15, Springer-Verlag, Berlin, 1988. |
[24] |
J. E. Pommersheim, Toric varieties, lattice points and Dedekind sums, Math. Ann., 295 (1993), 1-24.
doi: 10.1007/BF01444874. |
[25] |
J. E. Pommersheim, Products of cycles and the Todd class of a toric variety, J. Amer. Math. Soc., 9 (1996), 813-826.
doi: 10.1090/S0894-0347-96-00209-3. |
[26] |
J. Shaneson, Characteristic classes, lattice points and Euler-MacLaurin formulae, in Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Birkhäuser, Basel, 1995, 612-624. |
[27] |
D. Zagier, Equivariant Pontrjagin Classes and Applications to Orbit Spaces. Applications of the G-Signature Theorem to Transformation Groups, Symmetric Products and Number Theory, Lecture Notes in Mathematics, Vol. 290, Springer-Verlag, Berlin-New York, 1972. |
show all references
References:
[1] |
P. Aluffi, Classes de Chern pour variétés singulières, revisitées, C. R. Math. Acad. Sci. Paris, 342 (2006), 405-410.
doi: 10.1016/j.crma.2006.01.002. |
[2] |
A. Barvinok and J. E. Pommersheim, An algorithmic theory of lattice points in polyhedra, in New Perspectives in Algebraic Combinatorics (Berkeley, CA, 1996-97), Math. Sci. Res. Inst. Publ., 38, Cambridge Univ. Press, Cambridge, 1999, 91-147. |
[3] |
P. Baum, W. Fulton and R. MacPherson, Riemann-Roch for singular varieties, Inst. Hautes Études Sci. Publ. Math., 45 (1975), 101-145. |
[4] |
G. Barthel, J.-P. Brasselet and K.-H. Fieseler, Classes de Chern des variétés toriques singulières, C. R. Acad. Sci. Paris Sér. I Math., 315 (1992), 187-192. |
[5] |
J.-P. Brasselet, J. Schürmann and S. Yokura, Hirzebruch classes and motivic Chern classes of singular spaces, J. Topol. Anal., 2 (2010), 1-55.
doi: 10.1142/S1793525310000239. |
[6] |
M. Brion and M. Vergne, An equivariant Riemann-Roch theorem for complete, simplicial toric varieties, J. Reine Angew. Math., 482 (1997), 67-92. |
[7] |
S. E. Cappell, L. Maxim, J. Schürmann and J. L. Shaneson, Equivariant characteristic classes of complex algebraic varieties, Comm. Pure Appl. Math., 65 (2012), 1722-1769.
doi: 10.1002/cpa.21427. |
[8] |
S. E. Cappell and J. L. Shaneson, Genera of algebraic varieties and counting of lattice points, Bull. Amer. Math. Soc. (N.S.), 30 (1994), 62-69.
doi: 10.1090/S0273-0979-1994-00436-7. |
[9] |
S. E. Cappell and J. L. Shaneson, Euler-MacLaurin expansions for lattices above dimension one, C. R. Acad. Sci. Paris Sér. I Math., 321 (1995), 885-890. |
[10] |
D. Cox, The homogeneous coordinate ring of a toric variety, J. Alg. Geom., 4 (1995), 17-50. |
[11] |
D. Cox, J. Little and H. Schenck, Toric Varieties, Graduate Studies in Mathematics, 124, American Mathematical Society, Providence, RI, 2011. |
[12] |
V. I. Danilov, The geometry of toric varieties, Russian Math. Surveys, 33 (1978), 97-154.
doi: 10.1070/RM1978v033n02ABEH002305. |
[13] |
D. Edidin and W. Graham, Riemann-Roch for quotients and Todd classes of simplicial toric varieties, Comm. Algebra, 31 (2003), 3735-3752.
doi: 10.1081/AGB-120022440. |
[14] |
K. E. Feldman, Miraculous cancellation and Pick's theorem, in Toric Topology, Contemp. Math., 460, Amer. Math. Soc., Providence, RI, 2008, 71-86.
doi: 10.1090/conm/460/09011. |
[15] |
W. Fulton, Introduction to Toric Varieties, Annals of Mathematics Studies, 131, Princeton University Press, Princeton, NJ, 1993. |
[16] |
St. Garoufalidis and J. E. Pommersheim, Values of zeta functions at negative integers, Dedekind sums and toric geometry, J. Amer. Math. Soc., 14 (2001), 1-23.
doi: 10.1090/S0894-0347-00-00352-0. |
[17] |
I. Gessel, Generating functions and generalized Dedekind sums, Electron. J. Combin., 4 (1997), 17 pp. |
[18] |
M.-N. Ishida, Torus embeddings and de Rham complexes, in Commutative Algebra and Combinatorics (Kyoto, 1985), Adv. Stud. Pure Math., 11, North-Holland, Amsterdam, (1987), 111-145. |
[19] |
E. Materov, The Bott formula for toric varieties, Mosc. Math. J., 2 (2002), 161-182, 200. |
[20] |
L. Maxim and J. Schürmann, Characteristic classes of singular toric varieties, arXiv:1303.4454. |
[21] |
B. Moonen, Das Lefschetz-Riemann-Roch-Theorem für Singuläre Varietäten, Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn. Bonner Mathematische Schriften, 106, Universität Bonn, Mathematisches Institut, Bonn, 1978. |
[22] |
N. C. Leung and V. Reiner, The signature of a toric variety, Duke Math. J., 111 (2002), 253-286.
doi: 10.1215/S0012-7094-02-11123-5. |
[23] |
T. Oda, Convex Bodies and Algebraic Geometry. An Introduction to the Theory of Toric Varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 15, Springer-Verlag, Berlin, 1988. |
[24] |
J. E. Pommersheim, Toric varieties, lattice points and Dedekind sums, Math. Ann., 295 (1993), 1-24.
doi: 10.1007/BF01444874. |
[25] |
J. E. Pommersheim, Products of cycles and the Todd class of a toric variety, J. Amer. Math. Soc., 9 (1996), 813-826.
doi: 10.1090/S0894-0347-96-00209-3. |
[26] |
J. Shaneson, Characteristic classes, lattice points and Euler-MacLaurin formulae, in Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Birkhäuser, Basel, 1995, 612-624. |
[27] |
D. Zagier, Equivariant Pontrjagin Classes and Applications to Orbit Spaces. Applications of the G-Signature Theorem to Transformation Groups, Symmetric Products and Number Theory, Lecture Notes in Mathematics, Vol. 290, Springer-Verlag, Berlin-New York, 1972. |
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