Andrew R. Kustin --- Research

Vita: .pdf format

Macaulay2 scripts:

• SocDeg3.m2 This Package is described in the paper "Artinian Gorenstein algebras of socle degree three which have the weak Lefscetz property."

Recent Papers and preprints:

• "Artinian Gorenstein algebras of embedding dimension four and socle degree three over an arbitrary field" (with S. El Khoury) arXiv.
  
  
• "The weak Lefschetz property for Standard graded, Artinian Gorenstein algebras of embedding dimension four and socle degree three" J. Algebra 650 (2024), 80--122.
  
  
• "Quadratically presented grade three Gorenstein ideals" (with S. El Khoury) arXiv or J. Algebra 622 (2023), 258--290.
  
  
• "The syzygies of the ideal $(x_1^N,x_2^N,x_3^N,x_4^N)$ in the hypersurface ring defined by $x_1^n+x_2^n+x_3^n+x_4^n$ over any field" (with Rebecca R.G. and A. Vraciu) preprint or J. Algebra 615 (2023), 205--242.
  
  
• "The resolution of $(x^N,y^N,z^N,w^N)$" (with Rebecca R.G. and A. Vraciu) preprint or J. Algebra 590 (2022), 338--393.
  
  
• "Perfect modules with Betti numbers (2,6,5,1)" arXiv or J. Algebra 600 (2022), 71--124.
  
  
• "Using DG-methods to build a matrix factorization" arXiv or J. Commut. Algebra 14 (2022), 229--266.
  
  
• "Resolutions of length four which are Differential Graded Algebras" arXiv or J. Commut. Algebra 12 (2020), 509--538..
  
  
• "The structure of quasi-complete intersection ideals" (with L. Şega). arXiv or J. Algebra 632 (2023), 286--309.
  
  
• "Totally reflexive modules over rings that are close to Gorenstein" (with A. Vraciu). arXiv or J. Algebra, 571(2021), 190--231.
  
  
• "Poincaré series of compressed local Artinian rings with odd top socle degree" (with L. Şega and A. Vraciu). arXiv or J. Algebra 505 (2018), 383--419.
  
  
• "An alternating matrix and a vector, with application to Aluffi algebras" arXiv or J. Algebra 472, (2017), 115--145.
  
  
• "Canonical complexes associated to a matrix" arXiv or J. Algebra 460 (2016), 60--101.
  
  
• "Degree bounds for local cohomology" (with C. Polini and B. Ulrich) arXiv or Proc. Lond. Math. Soc. 121 (2020), 1251--1267.
  
  
• "A matrix of linear forms which is annihilated by a vector of indeterminates" (with C. Polini and B. Ulrich). arXiv or J. Algebra 469 (2017), 120--187.
  
  
• "The equations defining blowup algebras of height three Gorenstein ideals" (with C. Polini and B. Ulrich). arXiv, Algebra and Number Theory, 11 (2017), 1489--1525.
  
  
• "The Hilbert series of the ring associated to an almost alternating matrix" (C. Polini and B. Ulrich). arXiv or Comm. Algebra 44 (2016), 3053--3068.
  
  
• "Blowups and fibers of morphisms" (with C. Polini and B. Ulrich), arXiv or Nagoya Math. J. 224 (2016), 168--201.
  
  
• "The structure of Gorenstein-linear resolutions of Artinian algebras" (with S. El Khoury): arXiv or J. Algebra 453 (2016), 492--560.
  
  
• "The explicit minimal resolution constructed from a Macaulay inverse system" (with S. El Khoury): arXiv or J. Algebra 440 (2015), 145--186.
  
  
• "Minimal quasi-complete intersection ideals" (with L. Şega and A. Vraciu): arXiv or Illinois J. Math. 58 (2014), 867--889.
  
  
• "Artinian Gorenstein algebras with linear resolutions" (with S. El Khoury): arXiv or J. Algebra 420 (2014), 402--474.
  
  
• "Exact pairs of homogeneous zero divisors" (with J. Striuli and A. Vraciu): arXiv or J. Algebra 453 (2016), 221--248.
  
  
• "The bi-graded structure of Symmetric Algebras with applications to Rees rings" (with C. Polini and B. Ulrich): arXiv or J. Algebra 469 (2017), 188--250.
  
  
• "The Weak Lefschetz Property for monomial complete intersections" (with A. Vraciu): arXiv or Trans. Amer. Math. Soc., 366 (2014), 4571--4601.
  
  
• "Integral extensions and the $a$-invariant" (with C. Polini, and B. Ulrich): arXiv or Journal of Pure and Applied Algebra 216 (2012), 2800 -- 2806.
  
  
• "A study of singularities on rational curves via syzygies" (with D. Cox, C. Polini, and B. Ulrich): Memoirs of the AMS 222 (2013). arXiv or Memoirs of the AMS 222 (2013).
  
  
• "The resolution of the bracket powers of the maximal ideal in a diagonal hypersurface ring" (with H. Rahmati and A. Vraciu): or arXiv or Journal of Algebra 369 (2012), 256--321.
  
  
• "Rational Normal Scrolls and the Defining Equations of Rees Algebras" (with C. Polini and B. Ulrich): arXiv or Journal fur die reine und angewandte Mathematik 650 (2011), 23-65.
  
  
• "Divisors on Rational Normal Scrolls" (with C. Polini and B. Ulrich): arXiv or Journal of Algebra, Volume 322, (2009), 1748-1773.
  
  
• "Socle Degrees, Resolutions, and Frobenius Powers", (with B. Ulrich): arXiv or Journal of Algebra, 322, (2009), 25-41.
  
  
• "An explicit, characteristic-free, equivariant homology equivalence between Koszul complexes": Comm. in Algebra, vol. 36, no. 9, (2008), 3263--3316.
  
  
• "Socle degrees of Frobenius powers" (with A. Vraciu): arXiv Illinois Journal of Mathematics, vol. 51, no. 1 (2007), 185--208.
  
  
• "On the minimal free resolution of the universal ring for resolutions of length two" (with J.Weyman), : arXiv or Journal of Algebra, vol. 311, (2007), 435-462.
  
  
• "The resolution of the universal ring for modules of rank zero and projective dimension two", Journal of Algebra, vol. 310, (2007), 261--289: Final version .pdf file , or Final version .ps file , or 2002 draft .pdf version , or 2002 draft .ps version .
  
  
• "The cohomology of the Koszul complexes associated to the tensor product of two free modules" Comm. Alg. vol. 33, (2005), 467--495: . pdf version or ps version .
  
  
• "Complexes associated to two vectors and a rectangular matrix", Memoirs of the AMS, vol. 147, (2000), 1--81: .pdf version or .ps version .
  
  
• "Migliore-Peterson rings in the case that the reflexive sheaf has even rank", J. of Algebra, vol. 207, (1998), 572--615: .pdf version or .ps version .
  
  
• "Ideals associated to two sequences and a matrix", arXiv or Comm. in Algebra, vol. 23, (1995), 1047--1084.
  
  
• "Huneke-Ulrich almost complete intersections of Cohen-Macaulay type two", J. of Algebra, vol. 17, (1995), 373-429: .pdf version or .ps version .
  
  
• "The deviation two Gorenstein rings of Huneke and Ulrich", Commutative Algebra, 14--25 September 1992, ICTP, Trieste, Italy, World Scientific Publishing Co., River Edge, NJ, 1994, 140--163: .pdf version or .ps version .
  
  
• "Pfaffian identities, with applications to free resolutions, DG-Algebras, and algebras with straightening law", Contempory Math., vol. 159, (1994), 269--292: .pdf version or .ps version .
  
  
• "The Poincare series of every finitely generated module over a codimension four almost complete intersection is a rational function", (with S. Palmer Slattery), J. of Pure and Applied Algebra, vol. 95, (1994), 271--295: .pdf version or .ps version .
  
  
• "The minimal resolution of a codimension four almost complete intersection is a DG-algebra", J. of Algebra, vol. 168, (1994), 371--399: .pdf version or .ps version .
  
  
• "Classification of the Tor-algebras of codimension four almost complete intersections", Trans. Amer. Math. Soc.. vol.339, (1993), 61--85: .pdf version or .ps version .
  
  
• "Complexes which arise from a matrix and a vector: resolutions of divisors on certain varieties of complexes", J. of Algebra, vol. 158, (1993), 420--491: .pdf version or .ps version .
  
  
• "If the socle fits", (with B. Ulrich), J. of Algebra, vol. 147, (1992), 63--80 or .pdf version or .ps version .
  
  
• "Generating a residual intersection" (with M. Miller and B. Ulrich) J. Algebra 146 (1992), no. 2, 335–384. or .pdf version or .ps version .
  
  
• "The Lexicographic Sum of Cohen-Macaulay and Shellable Ordered Sets" (with J.~Griggs, J.~Ross, and J.~Stahl) Graphs Combin. 1 (1985), no. 2, 145--163. or .pdf version .