Comparison theorems for deformation functors via invariant theory

Collectanea Mathematica - Tập 70 Số 1 - Trang 1-32 - 2019
Jan Arthur Christophersen1, Jan O. Kleppe2
1Matematisk institutt, University of Oslo, Oslo, Norway
2Faculty of Technology, Art and Design, Oslo Metropolitan University, Oslo, Norway

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Altmann, K.: Minkowski sums and homogeneous deformations of toric varieties. Tohoku Math. J. (2) 47(2), 151–184 (1995)

Altmann, K.: One parameter families containing three-dimensional toric-Gorenstein singularities. In: Explicit Birational Geometry of 3-folds, London Mathemtical Society, Lecture Note Series, vol. 281, pp. 21–50, Cambridge University Press, Cambridge (2000)

André, M.: Homologie des algèbres commutatives. Springer, Berlin (1974)

Arzhantsev, I., Derenthal, U., Hausen, J., Laface, A.: Cox Rings, Cambridge Studies in Advanced Mathematics, vol. 144. Cambridge University Press, Cambridge (2015)

Batyrev, V.V.: Dual polyhedra and mirror symmetry for Calabi–Yau hypersurfaces in toric varieties. J. Algebr. Geom. 3(3), 493–535 (1994)

Batyrev, V.V., Cox, D.A.: On the Hodge structure of projective hypersurfaces in toric varieties. Duke Math. J. 75(2), 293–338 (1994)

Ballico, E., Ellia, P.: The maximal rank conjecture for nonspecial curves in ${ P}^3$. Invent. Math. 79(3), 541–555 (1985)

Cox, D.A., Katz, S.: Mirror Symmetry and Algebraic Geometry, Mathematical Surveys and Monographs, vol. 68. American Mathematical Society, Philadelphia (1999)

Cox, D.A., Little, J.B., Schenck, H.K.: Toric Varieties, Graduate Studies in Mathematics, vol. 124. American Mathematical Society, Philadelphia (2011)

Cox, D.A.: The homogeneous coordinate ring of a toric variety. J. Algebr. Geom. 4(1), 17–50 (1995)

Curtin, D.J.: Obstructions to deforming a space curve. Trans. Am. Math. Soc. 267, 83–94 (1981)

Delorme, C.: Espaces projectifs anisotropes. Bull. Soc. Math. France 103(2), 203–223 (1975)

Dolgachev, I.: Weighted Projective Varieties, Group Actions and Vector Fields (Vancouver, B.C., 1981), Lecture Notes in Mathematics, vol. 956, pp. 34–71. Springer, Berlin 1982 (1981)

Eisenbud, D., Mustaţǎ, M., Stillman, M.: Cohomology on toric varieties and local cohomology with monomial supports. J. Symb. Comput. 29(4–5), 583–600 (2000)

Fantechi, B., Manetti, M.: Obstruction calculus for functors of Artin rings, I. J. Algebra 202, 541–576 (1998)

Geramita, A.V., Maroscia, P., Roberts, L.G.: The Hilbert function of a reduced $k$-algebra. J. Lond. Math. Soc. (2) 28(3), 443–452 (1983)

Grothendieck, A.: Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2), Documents Mathématiques (Paris) [Mathematical Documents (Paris)], 4, Société Mathématique de France, Paris (2005)

Hartshorne, R.: Local Cohomology. A seminar given by A. Grothendieck, Harvard Univ., Fall 1961. Springer Lecture Notes in Mathematics, vol. 41. Springer, Berlin (1967)

Hartshorne, R.: Deformation Theory. Graduate Texts in Mathematics, vol. 257. Springer, New York (2010)

Haiman, M., Sturmfels, B.: Multigraded Hilbert schemes. J. Algebr. Geom. 13(4), 725–769 (2004)

Illusie, L.: Complexe cotangent et déformations. I, Lecture Notes in Mathematics, vol. 239. Springer, Berlin (1971)

Ilten, N.O.: Deformations of smooth toric surfaces. Manuscr. Math. 134(1–2), 123–137 (2011)

Kleppe, J.O.: Deformations of graded algebras. Math. Scand. 45, 205–231 (1979)

Kleppe, J.O.: The smoothness and the dimension of ${\rm PGor}(H)$ and of other strata of the punctual Hilbert scheme. J. Algebra 200(2), 606–628 (1998)

Laudal, O.A.: Formal Moduli of Algebraic Structures. Lecture Notes in Mathematics, vol. 754. Springer, Berlin (1979)

Lichtenbaum, S., Schlessinger, M.: The cotangent complex of a morphism. Trans. Am. Math. Soc. 128, 41–70 (1967)

Mumford, D., Fogarty, J., Kirwan, F.: Geometric Invariant Theory. Ergeb. Math. Grenzgebiete, vol. 34, 3rd edn. Springer, Berlin (1994)

Mukai, S.: An Introduction to Invariants and Moduli. Cambridge Studies in Advanced Mathematics, vol. 81. Cambridge University Press, Cambridge (2003)

Mumford, D.: Further pathologies in algebraic geometry. Am. J. Math. 84, 642–648 (1962)

Mustaţǎ, M.: Local cohomology at monomial ideals. J. Symb. Comput. 29(4–5), 709–720 (2000)

Piene, R., Schlessinger, M.: On the Hilbert scheme compactification of the space of twisted cubics. Am. J. Math. 107, 761–774 (1985)

Rim, D.S.: Equivariant $G$-structure on versal deformations. Trans. Am. Math. Soc. 257(1), 217–226 (1980)

Schlessinger, M.: Functors of Artin rings. Trans. Am. Math. Soc. 130, 208–222 (1968)

Schlessinger, M.: Rigidity of quotient singularities. Invent. Math. 14, 17–26 (1971)

Schlessinger, Michael: On rigid singularities. In: Proceedings of the Conference on Complex Analysis, Rice University Studies, vol. 59, pp. 147–162 (1973)

Sernesi, E.: Deformations of Algebraic Schemes. Springer, Berlin (2006)

Seshadri, C.S.: Quotient spaces modulo reductive algebraic groups. Ann. Math. 95, 511–556 (1972)

Stevens, J.: On canonical singularities as total spaces of deformations. Abh. Math. Sem. Univ. Hamburg 58, 275–283 (1988)

Tannenbaum, A.: Castelnuovo curves and unobstructed deformations. Math. Z. 174(2), 141–147 (1980)

Totaro, B.: Jumping of the nef cone for Fano varieties. J. Algebr. Geom. 21(2), 375–396 (2012)