Lyubeznik's Resolution and Rooted Complexes
Isabella Novik
DOI: 10.1023/A:1020838732281
Abstract
We describe a new family of free resolutions for a monomial ideal I, generalizing Lyubeznik”s construction. These resolutions are cellular resolutions supported on the rooted complexes of the lcm-lattice of I. Our resolutions are minimal for the matroid ideal of a finite projective space.
Pages: 97–101
Keywords: cellular resolutions; lcm-lattice; geometric lattice; matroid ideal
Full Text: PDF
References
1. E. Batzies and V. Welker, “Discrete Morse theory for cellular resolutions,” J. Reine Angew. Math. 543 (2002), 147-168.
2. D. Bayer and B. Sturmfels, “Cellular resolutions of monomial ideals,” J. Reine Angew. Math. 502 (1998), 123-140.
3. A. Bj\ddot orner and G. Ziegler, “Broken circuit complexes: Factorizations and generalizations,” J. Combin. Theory Ser. B 51 (1991), 96-126.
4. V. Gasharov, I. Peeva, and V. Welker, “The lcm-lattice in monomial resolutions,” Math. Res. Lett. 6 (1999), 521-532.
5. G. Lyubeznik, “A new explicit finite free resolution of ideals generated by monomials in an R-sequence,” J. Pure Appl. Algebra 51 (1988), 193-195.
6. I. Novik, A. Postnikov, and B. Sturmfels, “Syzygies of oriented matroids,” Duke Mathematical J. 111 (2002), 287-317.
7. R.P. Stanley, “Cohen-Macaulay complexes,” in Higher Combinatorics, M. Aigner (Ed.), Reidel, Dordrecht and Boston, 1977, pp. 51-62.
8. N. White (Ed.), Theory of Matroids, Cambridge University Press, 1986.
2. D. Bayer and B. Sturmfels, “Cellular resolutions of monomial ideals,” J. Reine Angew. Math. 502 (1998), 123-140.
3. A. Bj\ddot orner and G. Ziegler, “Broken circuit complexes: Factorizations and generalizations,” J. Combin. Theory Ser. B 51 (1991), 96-126.
4. V. Gasharov, I. Peeva, and V. Welker, “The lcm-lattice in monomial resolutions,” Math. Res. Lett. 6 (1999), 521-532.
5. G. Lyubeznik, “A new explicit finite free resolution of ideals generated by monomials in an R-sequence,” J. Pure Appl. Algebra 51 (1988), 193-195.
6. I. Novik, A. Postnikov, and B. Sturmfels, “Syzygies of oriented matroids,” Duke Mathematical J. 111 (2002), 287-317.
7. R.P. Stanley, “Cohen-Macaulay complexes,” in Higher Combinatorics, M. Aigner (Ed.), Reidel, Dordrecht and Boston, 1977, pp. 51-62.
8. N. White (Ed.), Theory of Matroids, Cambridge University Press, 1986.