Nicolas Perrin – Papers

Preprints:

  • (with M. Smirnov) On the big quantum cohomology of coadjoint varieties. arXiv.
  • (with A. Fanelli and L. Gruson) Rational curves on V5 and rational simple connectedness.  arXiv.
  • Semisimple quantum cohomology of some Fano varieties. arxiv.

To appear:

  • (with P.-E. Chaput) Affine symmetries in quantum cohomology: corrections and new results, to appear in Math. Research Letters, arXiv

Publications:

  • (with R. Gonzales, C. Pech and A. Samokhin) Geometry of horospherical varieties of Picard rank one. IMRN (2021). rnaa331. arXiv.
  • (with T. Hudson and T. Matsumura) Stability of Bott—Samelson Classes in Algebraic Cobordism. Springer Proc. Math. Stat., 332 (2020) 281–306. Schubert calculus and its applications in combinatorics and representation theory. arXiv.
  • Sanya lecure : geometry of spherical varieties. 2017. Acta Math. Sin. (Engl. Ser.) 34 (2018), no. 3, 371–416.PDF
  • (with A.S. Buch, P.-E. Chaput and L. Mihalcea) A Chevalley formula for the equivariant quantum K-theory of cominuscule varieties. Algebr. Geom. 5 (2018), no. 5, 568–595. PDF
  • (with J. A. Cruz Morales, A. Mellit, M. Smirnov and an appendix by A. Kuznetsov) On quantum cohomology of Grassmannians of isotropic lines, unfoldings of A_n-singularities, and Lefschetz exceptional collections. Ann. Inst. Fourier 69 (2019), no. 3, 955–991. PDF
  • (with M. Bender) Closures of B-conjugacy classes of 2-nilpotent matrices have rational singularities. Transform. Groups 24 (2019), no. 3, 741–768. PDF.
  • (with J. Hornbostel) Smooth Schubert varieties and generalized Schubert polynomials in algebraic cobordism of Grassmannians. Pacific J. Math. 294 (2018), no. 2, 401–422. PDF
  • (with A. Buch, P.-E. Chaput and L. Mihalcea) Projected Gromov-Witten varieties in cominuscule spaces. Proc. Amer. Math. Soc. 146 (2018), no. 9, 3647–3660.PDF
  • (with A. Buch, P.-E. Chaput and L. Mihalcea) Rational connectedness implies finiteness of quantum K-theory. Asian Journal of Mathematics. 20 (2016), no. 1, 117–122 PDF.
  • (with P. Achinger) Spherical multiple flag varieties. In Schubert Calculus – Osaka 2012. Advanced Studies of Pure Mathematics vol. 71, 2017. PDF.
  • Split subvarieties of group embeddings. Transactions of the AMS. 367 (2015), no. 12, 8421–8438 PDF.
  • Spherical varieties and Wahl’s conjecture. Annales de l’Institut Fourier. 64 (2014), no. 2, 739–751. PDF.
  • On the geometry of spherical varieties. Transform. Groups. 19 (2014), no.1, 171–223. PDF.
  • (with Jorge Caravantes) Formal properties in small codimension. Collectanea Mathematica. 65 (2014), no. 2, 251–256. PDF.
  • (with B. Pasquier) Elliptic curves on some homogeneous spaces. Doc. Math. 18 (2013), 679–706. PDF.
  • (with A. Buch, P.-E. Chaput and L.C. Mihalcea) Finiteness of cominuscule quantum K-theory. Annales de l’ENS 46 (2013) no.3, 477–494. PDF.
  • Elliptic curves on the spinor varieties. Cent. Eur. J. Math. 10 (2012), no. 4, 1393–1406. PDF.
  • (with P.-E. Chaput) Towards a Littlewood-Richardson rule for Kac-Moody homogeneous spaces. J. Lie Theory 22 (2012), no. 1, 17–80. PDF.
  • (with E. Smirnov) Springer fiber components in the two columns case for types A and D are normal. Bulletin de la SMF 140 (2012) no. 3, 309–333. PDF.  Erratum PDF.
  • (with S. Leidwanger) Study of some orthosymplectic Springer fibers. J. Algebra 335 (2011), 83–95. PDF.
  • (with P.-E. Chaput) On the quantum cohomology of adjoint varieties. Proc. Lond. Math. Soc. (3) 103 (2011), no. 2, 294–330. PDF. See also the companion file.
  • (with P.-E. Chaput) Rationality of some Gromov-Witten varieties and application to quantum K-theory. Commun. Contemp. Math. 13 (2011), no. 1, 67–90. PDF.
  • (with B. Pasquier) Local rigidity of quasi-regular varieties. Math. Zeit. 265 (2010), no. 3, 589–600. PDF.
  • (with P.-E. Chaput and L. Manivel) Quantum cohomology of minuscule homogeneous spaces III : semi-simplicity and consequences. Canad. J. Math. 62 (2010), no. 6, 1246–1263. PDF.
  • Small codimension subvarieties in homogeneous spaces. Indag. Math. (N.S.) 20 (2009), no. 4, 557–581. PDF.
  • (with P.-E. Chaput and L. Manivel) Affine symmetries of the equivariant quantum cohomology ring of rational homogeneous spaces. Mathematical Research Letters 16 (2009), 7–21. PDF.
  • Gorenstein locus of minuscule Schubert varieties. Advances in Math. 220 (2009), no. 2, 505–522. PDF.
  • (with P.-E. Chaput and L. Manivel) Quantum cohomology of minuscule homogeneous spaces. Transform. Groups 13 (2008), no. 1, 47–89. PDF.
  • (with P.-E. Chaput and L. Manivel) Quantum cohomology of minuscule homogeneous spaces II: hidden symmetries. IMRN 2007, no. 22. PDF.
  • Small codimension smooth subvarieties in even-dimensional homogeneous spaces with Picard group Z. CRAS 345 (2007), no. 3, 155–160. PDF.
  • Small resolutions of minuscule Schubert varieties. Compositio Math. 143 (2007), 1255–1312. PDF.
  • Rational curves on minuscule Schubert varieties. J. Algebra 294 (2005), no. 2, 431–462. PDF.
  • (with J. Almeida and L. Gruson) Courbes de genre 5 munies d’une involution sans point fixe. J. London Math. Soc. (2) 72 (2005), no. 3, 545–570. PDF.
  • Déformations de fibrés vectoriels sur les variétés de dimension 3. Manuscripta Math. 116 (2005), no. 4, 449–474 PDF.
  • Rational curves on homogeneous cones. Doc. Math. 9 (2004), 623–637 (electronic). PDF.
  • Deux composantes du bord de $I_3$. Bulletin de la SMF 130 (2002), no. 4, 537–572. PDF.
  • Limites de fibrés vectoriels dans $M_Q_3(0,2,0)$. CRAS 334 (2002), no. 9, 779–782. PDF.
  • Courbes rationnelles sur les variétés homogènes. Ann. Inst. Fourier 52 (2002), no. 1, 105–132. PDF.
  • Lieu singulier des surfaces rationnelles réglées. Math. Zeit. 241 (2002), no. 2, 375–396. PDF.
  • Une composante du bord des instantons de degré 3. CRAS 330 (2000), no. 3, 217–220. PDF.

Thesis:

– Habilitation (in french): Géometrie des espaces homogènes rationnels, courbes rationnelles et combinatoire. PDF.