Abstract
We study locally Cohen–Macaulay curves of low degree in the Segre threefold
Funding source: National Research Foundation of Korea
Award Identifier / Grant number: 2018R1C1A6004285
Award Identifier / Grant number: 2016R1A5A1008055
Funding statement: The first author is partially supported by MIUR and GNSAGA of INDAM (Italy). The third author is supported by the National Research Foundation of Korea(NRF) and a grant funded by the Korea government (MSIT) (No. 2018R1C1A6004285 and No. 2016R1A5A1008055).
Acknowledgements
We are deeply grateful to the anonymous referee for numerous corrections and suggestions that lead to better exposition of the article.
References
[1] D. Avritzer and I. Vainsencher, The Hilbert scheme component of the intersection of two quadrics, Comm. Algebra 27 (1999), no. 6, 2995–3008. 10.1080/00927879908826606Suche in Google Scholar
[2] E. Ballico and S. Huh, Stable sheaves on a smooth quadric surface with linear Hilbert bipolynomials, Sci. World J. 2014 (2014), Article ID 346126. 10.1155/2014/346126Suche in Google Scholar PubMed PubMed Central
[3]
E. Ballico, S. Huh and F. Malaspina,
Globally generated vector bundles on
[4] D. Bayer and D. Eisenbud, Ribbons and their canonical embeddings, Trans. Amer. Math. Soc. 347 (1995), no. 3, 719–756. 10.1090/S0002-9947-1995-1273472-3Suche in Google Scholar
[5] G. Bolondi, Irreducible families of curves with fixed cohomology, Arch. Math. (Basel) 53 (1989), no. 3, 300–305. 10.1007/BF01277068Suche in Google Scholar
[6] C. Bănică and O. Forster, Multiplicity structures on space curves, The Lefschetz Centennial Conference. Part I (Mexico City 1984), Contemp. Math. 58, American Mathematical Society, Providence (1986), 47–64. 10.1090/conm/058.1/860403Suche in Google Scholar
[7] J. Choi, K. Chung and M. Maican, Moduli of sheaves supported on quartic space curves, Michigan Math. J. 65 (2016), no. 3, 637–671. 10.1307/mmj/1472066152Suche in Google Scholar
[8] K. Chung, J. Hong and Y.-H. Kiem, Compactified moduli spaces of rational curves in projective homogeneous varieties, J. Math. Soc. Japan 64 (2012), no. 4, 1211–1248. 10.2969/jmsj/06441211Suche in Google Scholar
[9] K. Chung and Y.-H. Kiem, Hilbert scheme of rational cubic curves via stable maps, Amer. J. Math. 133 (2011), no. 3, 797–834. 10.1353/ajm.2011.0021Suche in Google Scholar
[10] W. Fulton and R. Pandharipande, Notes on stable maps and quantum cohomology, Algebraic Geometry (Santa Cruz 1995), Proc. Sympos. Pure Math. 62, American Mathematical Society, Providence (1997), 45–96. 10.1090/pspum/062.2/1492534Suche in Google Scholar
[11] R. Hartshorne, Connectedness of the Hilbert scheme, Inst. Hautes Études Sci. Publ. Math. (1966), no. 29, 5–48. 10.1007/BF02684803Suche in Google Scholar
[12] R. Hartshorne, Algebraic Geometry, Grad. Texts in Math. 52, Springer, New York, 1977. 10.1007/978-1-4757-3849-0Suche in Google Scholar
[13] R. Hartshorne and A. Hirschowitz, Smoothing algebraic space curves, Algebraic Geometry (Sitges 1983), Lecture Notes in Math. 1124, Springer, Berlin (1985), 98–131. 10.1007/BFb0074998Suche in Google Scholar
[14] R. Hartshorne, P. Lella and E. Schlesinger, Smooth curves specialize to extremal curves, Math. Ann. 361 (2015), no. 1–2, 459–476. 10.1007/s00208-014-1065-zSuche in Google Scholar
[15] R. Hartshorne, M. Martin-Deschamps and D. Perrin, Triades et familles de courbes gauches, Math. Ann. 315 (1999), no. 3, 397–468. 10.1007/s002080050323Suche in Google Scholar
[16] B. Kim and R. Pandharipande, The connectedness of the moduli space of maps to homogeneous spaces, Symplectic Geometry and Mirror Symmetry (Seoul 2000), World Scientific, River Edge (2001), 187–201. 10.1142/9789812799821_0006Suche in Google Scholar
[17] J. Kollár, Rational Curves on Algebraic Varieties, Ergeb. Math. Grenzgeb. (3) 32, Springer, Berlin, 1996. 10.1007/978-3-662-03276-3Suche in Google Scholar
[18] J. Li and G. Tian, Virtual moduli cycles and Gromov–Witten invariants of algebraic varieties, J. Amer. Math. Soc. 11 (1998), no. 1, 119–174. 10.1090/S0894-0347-98-00250-1Suche in Google Scholar
[19] J. Migliore, On linking double lines, Trans. Amer. Math. Soc. 294 (1986), no. 1, 177–185. 10.1090/S0002-9947-1986-0819941-3Suche in Google Scholar
[20] U. Nagel, R. Notari and M. L. Spreafico, The Hilbert scheme of degree two curves and certain ropes, Internat. J. Math. 17 (2006), no. 7, 835–867. 10.1142/S0129167X06003692Suche in Google Scholar
[21] S. Nollet, The Hilbert schemes of degree three curves, Ann. Sci. Éc. Norm. Supér. (4) 30 (1997), no. 3, 367–384. 10.1016/S0012-9593(97)89925-9Suche in Google Scholar
[22] S. Nollet and E. Schlesinger, Hilbert schemes of degree four curves, Compos. Math. 139 (2003), no. 2, 169–196. 10.1023/B:COMP.0000005083.20724.cbSuche in Google Scholar
[23] A. E. Parker, An elementary GIT construction of the moduli space of stable maps, Illinois J. Math. 51 (2007), no. 3, 1003–1025. 10.1215/ijm/1258131115Suche in Google Scholar
[24] R. Piene and M. Schlessinger, On the Hilbert scheme compactification of the space of twisted cubics, Amer. J. Math. 107 (1985), no. 4, 761–774. 10.2307/2374355Suche in Google Scholar
[25] E. Sernesi, On the existence of certain families of curves, Invent. Math. 75 (1984), no. 1, 25–57. 10.1007/BF01403088Suche in Google Scholar
[26] E. Sernesi, Deformations of Algebraic Schemes, Grundlehren Math. Wiss. 334, Springer, Berlin, 2006. Suche in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On the distribution of zeros of derivatives of the Riemann ξ-function
- Representations of constant socle rank for the Kronecker algebra
- Abstract bivariant Cuntz semigroups II
- Curves on Segre threefolds
- 𝒩(p, q, s)-type spaces in the unit ball of ℂn(II): Carleson measure and its application
- On a class of critical Robin problems
- On the description of multidimensional normal Hausdorff operators on Lebesgue spaces
- Spectral asymptotics for Krein–Feller operators with respect to 𝑉-variable Cantor measures
- Schneider–Siegel theorem for a family of values of a harmonic weak Maass form at Hecke orbits
- Modified energy method and applications for the well-posedness for the higher-order Benjamin–Ono equation and the higher-order intermediate long wave equation
- Some remarks on products of sets in the Heisenberg group and in the affine group
- Codimension growth of central polynomials of Lie algebras
- Unramified Whittaker functions for certain Brylinski–Deligne covering groups
- Tilting classes over commutative rings
Artikel in diesem Heft
- Frontmatter
- On the distribution of zeros of derivatives of the Riemann ξ-function
- Representations of constant socle rank for the Kronecker algebra
- Abstract bivariant Cuntz semigroups II
- Curves on Segre threefolds
- 𝒩(p, q, s)-type spaces in the unit ball of ℂn(II): Carleson measure and its application
- On a class of critical Robin problems
- On the description of multidimensional normal Hausdorff operators on Lebesgue spaces
- Spectral asymptotics for Krein–Feller operators with respect to 𝑉-variable Cantor measures
- Schneider–Siegel theorem for a family of values of a harmonic weak Maass form at Hecke orbits
- Modified energy method and applications for the well-posedness for the higher-order Benjamin–Ono equation and the higher-order intermediate long wave equation
- Some remarks on products of sets in the Heisenberg group and in the affine group
- Codimension growth of central polynomials of Lie algebras
- Unramified Whittaker functions for certain Brylinski–Deligne covering groups
- Tilting classes over commutative rings