SPINOR STRUCTURES ON FREE RESOLUTIONS OF CODIMENSION FOUR GORENSTEIN IDEALS

[1] J.F. Adams: Lectures on exceptional Lie groups, Chicago Lectures in Mathematics, University of Chicago

Press, Chicago, IL, 1996.

[2] W. Bruns and J. Herzog: Cohen-Macaulay rings, Cambridge Stud. Adv. Math. 39, Cambridge Univ. Press,

Cambridge, 1993.

[3] D.A. Buchsbaum and D. Eisenbud: Some structure theorems for finite free resolutions, Advances in Math.

12 (1974), 84–139.

[4] D.A. Buchsbaum and D. Eisenbud: Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension 3, Amer. J. Math. 99 (1977), 447–485.

[5] D.A. Buchsbaum and D. Eisenbud: What makes a complex exact?, J. Algebra 25 (1973), 259–268.

´ Cartan: The theory of spinors, The M.I.T. Press, Cambridge, Mass., 1967.

[6] E.

[7] E. Celikbas, J. Laxmi, W. Kra´s kiewicz and J. Weyman: The family of perfect ideals of codimension 3, of

type 2 with 5 generators, Proc. Amer. Math. Soc. 148 (2020), 2745–2755.

[8] R. Chiriv`ı and A. Maffei: Pfaffians and shuffling relations for the spin module, Algebr. Represent. Theory

16 (2013), 955-978.

[9] L.W. Christensen, O. Veliche and J. Weyman: Three takes on almost complete intersection ideals of grade

3; in Commutative Algebra, Springer, Cham, 2021, 219–281.

[10] P. Deligne: Notes on spinors; in Quantum fields and strings: a course for mathematicians 1, 2, Amer. Math.

Soc., Providence, RI, 1999, 99–135.

[11] W. Fulton and J. Harris: Representation theory, A first course, Graduate Texts in Mathematics 129, Reading

in Mathematics, Springer-Verlag, New York, 1991.

[12] R.G Daniel and M.E. Stillman: Macaulay2, a software system for research in algebraic geometry,

http://www.math.uiuc.edu/Macaulay2/

[13] R. Goodman and N.R. Wallach: Symmetry, representations, and invariants, Graduate Texts in Mathematics

255, Springer, New York, 2009.

[14] J.C. Jantzen: Representation of algebraic groups, Second Edition, Mathematical Surveys and Monographs

107, Amer. Math. Soc., Providence, RI, 2003.

[15] D. Knuth: Overlapping Pfaffians, Electron. J. Combin. 3 (1996), 147-159.

[16] A.R. Kustin and M. Miller: Constructing big Gorenstein ideals from small ones, J. Algebra 85 (1983),

303–322.

[17] A.R. Kustin and M. Miller: Algebra structure on minimal resolution of Gorenstein rings of embedding

codimension four, Math. Z. 173 (1980), 171–184.

[18] A.R. Kustin and M. Miller: Deformation and linkage of Gorenstein algebras, Trans. Amer. Math. Soc. 284

(1984), 501–534.

[19] A.R. Kustin and B. Ulrich: A family of complexes associated to almost alternating map with applications

to residual intersections, Mem. of Amer. Math. Soc. 95 (1992), no. 461.

[20] V. Lakshmibai and K.N. Raghavan: Standard monomial theory, Invariant theoretic approach, Encyclopaedia of Mathematical Sciences 137, Springer-Verlag, Berlin, 2008.

[21] M. Reid: Gorenstein in codimension 4: the general structure theory; in Algebraic Geometry in East Asia

(Taipei 2011), Adv. Stud. Pure Math. 65, Math. Soc. Japan, Tokyo, 2015, 201–227.

[22] J. Weyman: Cohomology of Vector Bundles and Syzygies, Cambridge Tracts in Mathematics 149, Cambridge University Press, Cambridge, 2003.

Spinor Structures on Free Resolutions

931

Ela Celikbas

School of Mathematical and Data Sciences, West Virginia University

Morgantown, WV 26506

USA

e-mail: ela.celikbas@math.wvu.edu

Jai Laxmi

School of Mathematics, Tata Institute of Fundamental Research

Mumbai-400005

India

e-mail: laxmiuohyd@gmail.com

jailaxmi@math.tifr.res.in

Jerzy Weyman

Department of Mathematics, University of Connecticut

Storrs, CT 06269

USA

e-mail: jerzy.weyman@uconn.edu

[Current Address:]

Instytut Matematyki, Uniwersytet Jagiello´nski

Krak´ow 30-348

Poland

e-mail: jerzy.weyman@uj.edu.pl

...