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DOUBLE LINES IN THE QUINTIC DEL PEZZO FOURFOLD

정기룡
대한수학회 (The Korean Mathematical Society)|2023.03|대한수학회보 (Bulletin of the KMS)|제60권 제2호|pp. 485-494|DOI 10.4134/BKMS.b220238

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키워드

Rational curvesFano varietydesingularizationintersection cohomology
주제분류수학

초록

Let $Y$ be the quintic del Pezzo $4$-fold defined by the linear section of $\textrm{Gr}(2,5)$ by $\mathbb{P}^7$. In this paper, we describe the locus of double lines in the Hilbert scheme of coincs in $Y$. As a corollary, we obtain the desigularized model of the moduli space of stable maps of degree $2$ in $Y$. We also compute the intersection Poincar\'e polynomial of the stable map space.

Abstract

Let $Y$ be the quintic del Pezzo $4$-fold defined by the linear section of $\textrm{Gr}(2,5)$ by $\mathbb{P}^7$. In this paper, we describe the locus of double lines in the Hilbert scheme of coincs in $Y$. As a corollary, we obtain the desigularized model of the moduli space of stable maps of degree $2$ in $Y$. We also compute the intersection Poincar\'e polynomial of the stable map space.

참고문헌 (13)

  1. K. Chung, "Desingularization of Kontsevich's compactification of twisted cubics in V5" (2022), Manuscripta Mathematica
  2. Kiryong CHUNG, "Compactified moduli spaces of rational curves in projective homogeneous varieties", Journal of the Mathematical Society of Japan, 64(4) (2012), Mathematical Society of Japan (Project Euclid)[DOI]
  3. Kiryong Chung, "Geometry of moduli spaces of rational curves in linear sections of Grassmannian Gr(2,5)", Journal of Pure and Applied Algebra, 222(4), pp.868~888 (2018), Elsevier BV[DOI]
  4. Kiryong Chung, "Hilbert scheme of rational cubic curves via stable maps", American Journal of Mathematics, 133(3), pp.797~834 (2011), Project MUSE[DOI]
  5. Kiryong Chung, "Mori's Program for the Moduli Space of Conics in Grassmannian", Taiwanese Journal of Mathematics, 21(3) (2017), The Mathematical Society of the Republic of China[DOI]
  6. Akira Fujiki, "Supplement to "On the Inverse of Monoidal Transformation"", Publications of the Research Institute for Mathematical Sciences, 7(3), pp.637~644 (1971), European Mathematical Society - EMS - Publishing House GmbH[DOI]
  7. W. Fulton, "Notes on stable maps and quantum cohomology", Proc. Sympos. Pure Math, 62, pp.45~96 (1997), Amer. Math. Soc., Providence
  8. "Macaulay2, a software system for research in algebraic geometry"[URL]
  9. Alexander G. Kuznetsov, "Hilbert schemes of lines and conics and automorphism groups of Fano threefolds", Japanese Journal of Mathematics, 13(1), pp.109~185 (2018), Springer Science and Business Media LLC[DOI]
  10. L. G. Maxim, "Intersection homology and perverse sheaves, with applications to singularities" (2018), Book Project
  11. Y. Prokhorov, "Compactifications of ℂ4 of index 3, In Algebraic geometry and its applications (Yaroslavl , 1992)", Aspects Math, E25, pp.159~169 (1994), Vieweg
  12. Yuri Prokhorov, "Examples of cylindrical Fano fourfolds", European Journal of Mathematics, 2(1), pp.262~282 (2015), Springer Science and Business Media LLC[DOI]
  13. Victor Vladimirovich Przyjalkowski, "Fano threefolds with infinite automorphism groups", Известия Российской академии наук. Серия математическая, 83(4), pp.226~280 (2019), Steklov Mathematical Institute[DOI]

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