Toward free resolutions over scrolls
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- by Laura Felicia Matusevich and Aleksandra Sobieska PDF
- Proc. Amer. Math. Soc. 148 (2020), 5071-5086 Request permission
Abstract:
Let $R=\Bbbk [x]/I$ where $I$ is the defining ideal of a rational normal $k$-scroll. We compute the Betti numbers of the ground field $\Bbbk$ as a module over $R$. For $k=2$, we give the minimal free resolution of $\Bbbk$ over $R$.References
- Winfried Bruns, Jürgen Herzog, and Udo Vetter, Syzygies and walks, Commutative algebra (Trieste, 1992) World Sci. Publ., River Edge, NJ, 1994, pp. 36–57. MR 1421076
- David A. Buchsbaum and David Eisenbud, What makes a complex exact?, J. Algebra 25 (1973), 259–268. MR 314819, DOI 10.1016/0021-8693(73)90044-6
- Michael L. Catalano-Johnson, The resolution of the ideal of $2\times 2$ minors of a $2\times n$ matrix of linear forms, J. Algebra 187 (1997), no. 1, 39–48. MR 1425558, DOI 10.1006/jabr.1997.6801
- David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960, DOI 10.1007/978-1-4612-5350-1
- R. Fröberg, Koszul algebras, Advances in commutative ring theory (Fez, 1997) Lecture Notes in Pure and Appl. Math., vol. 205, Dekker, New York, 1999, pp. 337–350. MR 1767430
- R. Fröberg, Koszul algebras, Advances in commutative ring theory (Fez, 1997) Lecture Notes in Pure and Appl. Math., vol. 205, Dekker, New York, 1999, pp. 337–350. MR 1767430
- Ralph Fröberg, Determination of a class of Poincaré series, Math. Scand. 37 (1975), no. 1, 29–39. MR 404254, DOI 10.7146/math.scand.a-11585
- Vesselin Gasharov, Noam Horwitz, and Irena Peeva, Hilbert functions over toric rings, Michigan Math. J. 57 (2008), 339–357. Special volume in honor of Melvin Hochster. MR 2492457, DOI 10.1307/mmj/1220879413
- Andrew R. Kustin, Claudia Polini, and Bernd Ulrich, Divisors on rational normal scrolls, J. Algebra 322 (2009), no. 5, 1748–1773. MR 2543633, DOI 10.1016/j.jalgebra.2009.05.010
- Hop D. Nguyen, Phong Dinh Thieu, and Thanh Vu, Koszul determinantal rings and $2 \times e$ matrices of linear forms, Michigan Math. J. 64 (2015), no. 2, 349–381. MR 3359030, DOI 10.1307/mmj/1434731928
- Irena Peeva, Infinite free resolutions over toric rings, Syzygies and Hilbert functions, Lect. Notes Pure Appl. Math., vol. 254, Chapman & Hall/CRC, Boca Raton, FL, 2007, pp. 233–247. MR 2309932, DOI 10.1201/9781420050912
- Irena Peeva, Victor Reiner, and Bernd Sturmfels, How to shell a monoid, Math. Ann. 310 (1998), no. 2, 379–393. MR 1602024, DOI 10.1007/s002080050152
- Sonja Petrović, On the universal Gröbner bases of varieties of minimal degree, Math. Res. Lett. 15 (2008), no. 6, 1211–1221. MR 2470395, DOI 10.4310/MRL.2008.v15.n6.a11
Additional Information
- Laura Felicia Matusevich
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
- MR Author ID: 632562
- Email: laura@math.tamu.edu
- Aleksandra Sobieska
- Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
- MR Author ID: 1176078
- ORCID: 0000-0002-1150-3725
- Email: asobieska@math.wisc.edu
- Received by editor(s): March 28, 2019
- Received by editor(s) in revised form: February 24, 2020
- Published electronically: September 24, 2020
- Additional Notes: The authors were partially supported by NSF grant DMS-1500832.
- Communicated by: Jerzy Weyman
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 5071-5086
- MSC (2010): Primary 13D02, 16S37; Secondary 16S36, 13F55
- DOI: https://doi.org/10.1090/proc/15150
- MathSciNet review: 4163823