Andrew R. Kustin --- Research

Vita: .pdf format or .ps format

Recent Papers and preprints:

• ``The Weak Lefschetz Property for monomial complete intersections'' (with A. Vraciu): You may find the paper on the arXiv.
  
  
• ``Integral extensions and the $a$-invariant'' (with C. Polini, and B. Ulrich): .pdf version, preprint. You may find the paper on the arXiv.
  
  
• ``A study of singularities on rational curves via syzygies'' (with D. Cox, C. Polini, and B. Ulrich): Revised, January 30, 2012, to appear in the Memoirs of the AMS. You may find the paper on the arXiv.
  
  
• ``The resolution of the bracket powers of the maximal ideal in a diagonal hypersurface ring'' (with H. Rahmati and A. Vraciu): .pdf version, preprint. You may find the paper on the arXiv.
  
  
• ``Rational Normal Scrolls and the Defining Equations of Rees Algebras'' (with C. Polini and B. Ulrich): .pdf version or .ps version, preprint. You may find the paper on the arXiv. Journal fur die reine und angewandte Mathematik 650 (2011), 23-65.
  
  
• ``Divisors on Rational Normal Scrolls'' (with C. Polini and B. Ulrich): .pdf version or .ps version, preprint. You may find the paper on the arXiv. Journal of Algebra, Volume 322, (2009), 1748-1773.
  
  
• ``Socle Degrees, Resolutions, and Frobenius Powers'', (with B. Ulrich): .pdf version or .ps version, preprint. You may find the paper on the arXiv. Journal of Algebra, Volume 322, (2009), 25-41.
  
  
• ``An explicit, characteristic-free, equivariant homology equivalence between Koszul complexes'': Comm. in Algebra, vol. 36, no. 9, (2008), 3263--3316.
  Earlier versions of this paper were called: ``Divisors over determinantal rings defined by two by two minors'' .pdf version or .ps version
  and ``An explicit quasi-isomorphism between Koszul complexes''. The maps in the earlier versions of the paper are not equivariant.
  
  
• ``Socle degrees of Frobenius powers'' (with A. Vraciu): . pdf version or ps version . 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), Journal of Algebra, vol. 311, (2007), 435-462: . pdf version or ps version .
  
  
• ``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'', Comm. in Algebra, vol. 23, (1995), 1047--1084: .pdf version or .ps version .
  
  
• ``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: .pdf version or .ps version . J. of Algebra, vol. 146, (1992), 335--384: .pdf version or .ps version .

Various Lectures:

• "The generic Hilbert-Burch matrix" , AMS meeting, Statesboro, Georgia, March, 2011.