Partial differential Chow forms and a type of partial differential Chow varieties

References

• Brownawell, W. D. (1987). Bounds for the degrees in the Nullstellensatz. Ann. Math. 126(3):577–591. DOI: 10.2307/1971361.
   Web of Science ®Google Scholar
• Buium, A., Cassidy, P., et al. (1998). Differential algebraic geometry and differential algebraic groups. In: H. Bass, ed. Selected Works of Ellis Kolchin, with Commentary. Providence, RI: American Mathematical Society, pp. 567–636.
   Google Scholar
• Chow, W.-L., van der Waerden, B. L. (1937). Zur algebraischen Geometrie. IX. Math. Ann. 113(1):692–704. DOI: 10.1007/BF01571660.
   Google Scholar
• Eisenbud, D., Harris, J. (2016). 3264 And All That—A Second Course in Algebraic Geometry. Cambridge: Cambridge University Press.
   Google Scholar
• Eisenbud, D., Schreyer, F.-O., Weyman, J. (2003). Resultants and Chow forms via exterior syzygies. J. Am. Math. Soc. 16(03):537–579. DOI: 10.1090/S0894-0347-03-00423-5.
   Google Scholar
• Freitag, J. (2015). Bertini theorems for differential algebraic geometry. ArXiv:1211.0972v3.
   Google Scholar
• Freitag, J., León Sánchez, O. (2016). Effective uniform bounding in partial differential fields. Adv. Math. 288:308–336. DOI: 10.1016/j.aim.2015.10.013.
   Web of Science ®Google Scholar
• Freitag, J., Li, W., Scanlon, T., Johnson, W. (2017). Differential Chow varieties exist. With an appendix by William Johnson. J. London Math. Soc. 95(1):128–156. DOI: 10.1112/jlms.12002.
   Google Scholar
• Gao, X.-S., Li, W., Yuan, C.-M. (2013). Intersection theory in differential algebraic geometry: generic intersections and the differential Chow form. Trans. Am. Math. Soc. 365(9):4575–4632. DOI: 10.1090/S0002-9947-2013-05633-4.
   Web of Science ®Google Scholar
• Harris, J. (1992). Algebraic Geometry: A First Course (Graduate Texts in Mathematics), Vol. 133. New York: Springer.
   Google Scholar
• Heintz, J. (1983). Definability and fast quantifier elimination in algebraically closed fields. Theoret. Comput. Sci. 24(3):239–277. DOI: 10.1016/0304-3975(83)90002-6.
   Web of Science ®Google Scholar
• Hodge, W., Pedoe, D. (1994). Methods of Algebraic Geometry, Vol. 1. Cambridge: Cambridge University Press.
   Google Scholar
• Hodge, W. V. D., Pedoe, D. (1994). Methods of Algebraic Geometry, Vol. 2. Cambridge: Cambridge University Press.
   Google Scholar
• Jeronimo, G., Krick, T., Sabia, J., Sombra, M. (2004). The computational complexity of the Chow form. Found. Comput. Math. 4(1):41–117. DOI: 10.1007/s10208-002-0078-2.
   Web of Science ®Google Scholar
• Kolchin, E. R. (1964). The notion of dimension in the theory of algebraic differential equations. Bull. Am. Math. Soc. 70(4):570–573. DOI: 10.1090/S0002-9904-1964-11203-9.
   Web of Science ®Google Scholar
• Kolchin, E. R. (1973). Differential Algebra and Algebraic Groups. New York, NY: Academic Press.
   Google Scholar
• Kondratieva, M. V., Levin, A. B., Mikhalev, A. V., Pankratiev, E. V. (1999). Differential and difference dimension polynomials. Mathematics and Its Applications, Vol. 461. Dordrecht: Kluwer Academic Publishers.
   Google Scholar
• León Sánchez, O. (2012). Geometric axioms for differentially closed fields with several commuting derivations. J. Algebra 362:107–116. DOI: 10.1016/j.jalgebra.2012.03.043.
   Web of Science ®Google Scholar
• Li, W., Gao, X.-S., Yuan, M. (2011). Sparse differential resultant. Presented at the ISSAC 2011—Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation, ACM, New York, June 8–11 (San Jose, California, USA), pp. 225–232. DOI: 10.1145/1993886.1993922.
   Google Scholar
• Li, W., Gao, X.-S. (2012). Chow form for projective differential variety. J. Algebra 370:344–360. DOI: 10.1016/j.jalgebra.2012.07.047.
   Web of Science ®Google Scholar
• Li, W., Yuan, C.-M., Gao, X.-S. (2015). Sparse differential resultant for Laurent differential polynomials. Found. Comput. Math. 15(2):451–517. DOI: 10.1007/s10208-015-9249-9.
   Web of Science ®Google Scholar
• McGrail, T. (2000). The model theory of differential fields with finitely many commuting derivations. J. Symb. Log. 65(2):885–913. DOI: 10.2307/2586576.
   Web of Science ®Google Scholar
• Philippon, P. (1986). Critères pour l’indpendance algbrique. Publications Mathématiques de L’institut. Des. Hautes. Scientifiques. 64(1):5–52. DOI: 10.1007/BF02699191.
   Google Scholar
• Pierce, D. (2014). Fields with several commuting derivations. J. Symb. Log. 79(01):1–19. DOI: 10.1017/jsl.2013.19.
   Google Scholar
• Ritt, J. F. (1950). Differential Algebra. New York, NY: American Mathematical Society.
   Google Scholar
• Wu, W.-T. (1989). On the foundation of algebraic differential polynomial geometry. Syst. Sci. Math. Sci. 2(4):289–312.
   Google Scholar