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Aluffi, Paolo

Computing characteristic classes of projective schemes. (English) Zbl 1074.14502

J. Symb. Comput. 35, No. 1, 3-19 (2003).
Summary: We discuss an algorithm computing the push-forward to projective space of several classes associated to a (possibly singular, reducible, non-reduced) projective scheme. For example, the algorithm yields the topological Euler characteristic of the support of a projective scheme \(S\), given the homogeneous ideal of \(S\). The algorithm has been implemented in Macaulay2.

Cited in 29 Documents

MSC:

14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
14Q15 Computational aspects of higher-dimensional varieties
68W30 Symbolic computation and algebraic computation

Keywords:

topological Euler characteristic; Macaulay2

Software:

Macaulay2; CSM-A
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\textit{P. Aluffi}, J. Symb. Comput. 35, No. 1, 3--19 (2003; Zbl 1074.14502)
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References:

[1] Aluffi, P., Macpherson’s and fulton’s Chern classes of hypersurfaces, Int. math. res. notices, 11, 455-465, (1994) · Zbl 0839.14035
[2] Aluffi, P., Characteristic classes of discriminants and enumerative geometry, Comm. algebra., 26, 3165-3193, (1998) · Zbl 0934.14039
[3] Aluffi, P., Chern classes for singular hypersurfaces, Trans. am. math. soc., 351, 3989-4026, (1999) · Zbl 0972.57015
[4] Aluffi, P., 2002. Inclusion-exclusion and Segre classes. FSU02-11, arXiv:math.AG/0203122 (will appear in Comm. Algebra, issue dedicated to Steven Kleiman)
[5] Aluffi, P.; Faber, C., Linear orbits of d-tuples of points in {\bfp}1, J. reine angew. math., 445, 205-220, (1993) · Zbl 0781.14036
[6] Brasselet, J.-P., From Chern classes to Milnor classes—a history of characteristic classes for singular varieties, (), 31-52 · Zbl 1036.32022
[7] Eisenbud, D.; Grayson, D.; Stillman, M.; Sturmfels, B., Computations in algebraic geometry with Macaulay 2, (2002), Springer Berlin · Zbl 0973.00017
[8] Fulton, W., Intersection theory, (1984), Springer Berlin · Zbl 0541.14005
[9] Kennedy, G., Macpherson’s Chern classes of singular algebraic varieties, Comm. algebra., 18, 2821-2839, (1990) · Zbl 0709.14016
[10] MacPherson, R.D., Chern classes for singular algebraic varieties, Ann. math. (2), 100, 423-432, (1974) · Zbl 0311.14001
[11] Micali, A., Sur LES algèbres universelles, Ann. inst. Fourier (Grenoble), 14, 33-87, (1964) · Zbl 0152.02602
[12] Parusiński, A., A generalization of the Milnor number, Math. ann., 281, 247-254, (1988) · Zbl 0617.32012
[13] Parusiński, A.; Pragacz, P., Characteristic classes of hypersurfaces and characteristic cycles, J. algebraic. geom., 10, 63-79, (2001) · Zbl 1072.14505
[14] Schürmann, J., 2002. A generalized Verdier-type Riemann-Roch theorem for Chern-Schwartz-MacPherson classes, arXiv:math.AG/0202175
[15] Vasconcelos, W.V., 1998. Computational Methods in Commutative Algebra and Algebraic Geometry (with chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman. Springer, Berlin) · Zbl 0896.13021
[16] Walther, U., Algorithmic determination of the rational cohomology of complex varieties via differential forms, (), 185-206 · Zbl 1079.14507
[17] Yokura, S., On a verdier-type riemann – roch for chern – schwartz – macpherson class, Topology appl., 94, 315-327, (1999), Special issue in memory of B.J. Ball · Zbl 0928.14010
[18] Yokura, S., On characteristic classes of complete intersections, (), 349-369 · Zbl 0966.14004
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