Jerome William Hoffman

Publications


  1. The Hodge theory of flat vector bundles on a complex torus, Transactions. of the A.M.S., 271, 1982, 117 - 131.
  2. An example in the theory of degenerating algebraic curves, Boll. U. M. I., 1 - B, 1982, 885 - 917.
  3. Counterexamples to the lifting problem for singularities, Comm. in Algebra, 11, 1983, 523 - 549.
  4. The Hodge theory of stable curves, Mem. Amer. Math. Soc. 51 (1984) no. 308, 91 pages.
  5. On Kollar's vanishing theorems I, Duke Math. J. 59, 1989, 521 - 535.
  6. Heller's Axioms for homotopy theory, Cahiers de Topologie et Geometrie Differentielle Categoriques, vol XXXVII - 3 (1996) 179 - 255.
  7. (with Morales, J.) Arithmetic of binary cubic forms, L'Enseignement Mathematique, 46 (2000), 61-94.
  8. (with Weintraub, S. H.) Cohomology of the Siegel modular group of degree two and level four, Mem. Amer. Math. Soc., 133 (1998), no. 631, 61-75..
  9. (with S. H. Weintraub) Four dimensional symplectic geometry over the field with three elements and moduli spaces of abelian surfaces, Note di Matematica, 20, (2000/2001), 111-157.
  10. Proceedings of the Conference on Quadratic Forms and Related Topics. Held at Louisiana State University, Baton Rouge, LA, March 26--30, 2001. Edited by J. W. Hoffman, J. Hurrelbrink, J. Morales, R. Perlis and P. van Wamelen. Doc. Math. 2001, Extra Vol. Documenta Mathematica, Bielefeld, 2001. pp. i--iv and 1--251
  11. (with S. H. Weintraub) The Siegel modular variety of degree two and level three, Transactions of the A. M. S. 353 (2001) 3267-3305.
  12. (with J. Madden and Hong Zhang) Pseudozeros of multivariate polynomials, Mathematics of Computation 72 (2003), no. 242, 975--1002
  13. Remarks on the zeta function of a graph, in Dynamical Systems and Differential Equations, a supplement volume of Discrete and Continuous Dynamical Systems, Wei Feng, Shouchuan Hu and Xin Lu (eds.), (2003), 413-422.
  14. (with S. H. Weintraub) Cohomology of the boundary of Siegel modular varieties of degree two, with applications, Fundamenta Mathematicae, 178 (2003), 1-47.
  15. (with Wang, H.- H.) Castelnuovo-Mumford regularity in biprojective spaces,  Advances in Geometry 4, (2004), 513-536.

  

   16    (with Adkins, W. and Wang, H.)  Equations of parametric surfaces with base points via syzygies, Journal of Symbolic Computation, 39, (2005), 73-101. 


   17  (with A. Deitmar)   The Ihara-Selberg zeta function for PGL_3 and Hecke operators.  International J. of Math. 17, (2006) 1-13. 


   18  (with Wang, H.) Curvilinear base points, local complete intersection and Koszul syzygies in biprojective spaces. Trans. Amer. Math. Soc.  358  (2006),  no. 8, 3385--3398.


   19  (with Wang, H.) Regularity and resolutions for multigraded modules, Journal of Algebra and its Applications, vol. 6, no. 4 (2007) 703-730. 


   20 Cox, David; Hoffman, J. William; Wang, Haohao, Syzygies and the Rees algebra. J. Pure Appl. Algebra  212  (2008),  no. 7, 1787--1796. 


   21 (with Liqun Fang, Ben Linowitz, Andrew Rupinski, Helena Verrill) Modular forms on noncongruence subgroups and Atkin-Swinnerton-Dyer relations.

      Journal of Experimental Mathematics, 19 no. 1, (2010), 1-27. 


   22  Hoffman, J. William; Wang, Haohao; Jia, Xiaohong; Goldman, Ron Minimal generators for the Rees algebra of rational space curves of type (1,1,d-2)

      Eur. J. Pure Appl. Math.  3  (2010),  no. 4, 602--632.


  23 Hoffman, J. William; Wang, Haohao,  Defining equations of the Rees algebra of certain parametric surfaces.  Journal of Algebra and its Applications.  9 (2010),  no. 6, 1033-1046.


  24 (with Ling Long and Helena Verrill)  On \ell-adic representations for a space of noncongruence cusp forms,  Proc. Amer. Math. Soc. 140 (2012), 1569-1584.


 25 (with Hongyu He) Picard groups of Siegel modular 3-folds and \theta-liftings. Journal of Lie Theory, (2012)(3), 769-801. 


  26 (with F.T. Hawwa and Haohao Wang)   Koszul Duality for Multigraded Algebras, European Journal of Pure and Applied Mathematics, vol. 5, no. 4, 2012, 511-539.


  27 (with Haohao Wang) 7-gons and genus 3 hyperelliptic curves, RACSAM - Revista de la Real Academia de Ciencias Exactas, F’sicas y Naturales. Serie A. Matem‡ticas, Vol. 107(2013), 35-52.


  28  Hoffman, Jerome W.; Liang, Z.; Sakai, Yukiko; Zhao, Xuezhi, Homotopy minimal period self-maps on flat manifolds. Adv. Math. 248 (2013), 324--334


  29 (with Haohao Wang) A note on quadratically parametrized surfaces, Algebra Colloquium, Vol. 21 (2014), 461--476.


  30 (with Haohao Wang)  Note on the regularity of the radical of ideals, International Electronic Journal of Algebra, 17, (2015), 154-160.


  31 Hoffman, J. William; Liang, Zhibin; Sakai, Yukiko; Wang, Haohao Genus 3 curves whose Jacobians have endomorphisms by \mathbf{Q} (\zeta _7 +\bar{\zeta}_7)}. J. Symbolic Comput. 74 (2016), 561--577.


  32   Hoffman, Jerome; Long, Ling; Mahlburg, Karl; Morales, Jorge; Oporowski, Bogdan; Perlis, Robert; Swisher, Holly,

 Preface [Special issue on applications of automorphic forms in number theory and combinatorics in honor of the lifelong work of Wen-Ching Winnie Li]. J. Number Theory 161 (2016), 1--16.


 33  Benjamin Dribus, Jerome William Hoffman, Sen Yang,  Tangents to Chow groups: on a question of Green-Griffiths, Boll. Unione Mat. Ital. (2018) 11: 205-244.


 34 Hoffman, J. William; Liang, Dun; Liang, Zhibin; Okazaki, Ryotaro; Sakai, Yukiko; Wang, Haohao,  Genus 3 curves whose Jacobians have endomorphisms by 

\mathbf{Q} (\zeta _7 +\bar{\zeta}_7), II}.  Tokyo J. Math. 42 (2019), no. 1, 185--218.


 35 J. W. Hoffman, Xiaohong Jia, Haohao Wang, Quaternion rational surfaces,  J. Commut. Algebra 12 (2020), no. 2, 237--261.


 36  J. W. Hoffman, Haohao Wang,  Minimal Free Resolution of A Family of Generic Monomial Ideals, Algebra, Groups and Geometries, Vol. 38, 215-234 (2022).  


 37 J. W. Hoffman, Haohao Wang, A study of a family of monomial ideals, Journal of Algebra and Its Applications,  22 (2023) no 3, Paper No. 2350068, 23 pp.


  38  Hoffman, J. William and Wang, Haohao, Algebraic and geometric properties of a family of rational curves, International Electronic Journal of Geometry, 17, 2024, 2, 306--316.


 39. Hoffman, J. William and Wang, Haohao, Quaternions associated to curves and surfaces, Palest. J. Math., 13, 2024, 43-54.



                                                                                                                 Preprints



  1 (with  Winnie Li, Ling, Long, Fang-Ting Tu), Traces of Hecke Operators via Hypergeometric Character Sums,  arXiv:2408.02918.


 2 (with Fang-Ting Tu), QM abelian varieties, hypergeometric character sums and modular forms, arXiv:2408.06562 


3  (with  Fang-Ting Tu), Transformations of Hypergeometric Motives, arXiv: 2003.05031


3  (with Haohao Wang) Computational and Theoretical Aspects of Rational Parametrization of Generalized Tubular Surfaces, 16pp.