On the Effective Cone of Blown-up at n + 3 Points

References

• [Alexander and Hirschowitz 95] J. Alexander and A. Hirschowitz. “Polynomial Interpolation in Several Variables.” J. Algebraic Geom. 4: 2 (1995), 201–222.
   Google Scholar
• [Arzhantsev et al. 15] I. Arzhantsev, U. Derenthal, J. Hausen, A. Laface. Cox rings, Cambridge Studies in Advanced Mathematics 144. p. 530. Cambridge: Cambridge University Press viii, 2015.
   Google Scholar
• [Bocci 05] C. Bocci. “Special Effect Varieties in Higher Dimension.” Collectanea Mathematica 56: 3 (2005), 299–326. ISSN: 0010-0757.
   Web of Science ®Google Scholar
• [Bocci 10] C. Bocci. “Special Effect Varieties and (−1)-Curves.” Rocky Mountain J. Math. 40: 2 (2010), 397–419.
   Web of Science ®Google Scholar
• [Brambilla et al. 15] M. C. Brambilla, O. Dumitrescu and E. Postinghel. “On A Notion of Speciality of Linear Systems in .” Trans. Am. Math. Soc. 367 (2015), 5447–5473.
   Web of Science ®Google Scholar
• [Brambilla et al.] M. C. Brambilla, O. Dumitrescu and E. Postinghel. “On Linear Systems of with Nine Base Points.” Ann. Mat. Pura Appl. DOI: 10.1007/s10231-015-0528-5.
   Web of Science ®Google Scholar
• [Brambilla and Ottaviani 08] M. C. Brambilla and G. Ottaviani. “On The Alexander-Hirschowitz Theorem.” J. Pure Appl. Algebra. 212: 5 (2008), 1229–1251.
   Web of Science ®Google Scholar
• [Cacciola et al. 11] S. Cacciola, M. Donten-Bury, O. Dumitrescu, A. Lo Giudice, and J. Park. “Cones of Divisors of Blow-ups of Projective Spaces.” Matematiche (Catania) 66: 2 (2011), 153–187.
   Google Scholar
• [Carlini and Catalisano 07] E. Carlini and M. V. Catalisano. “Existence Results for Rational Normal Curves.” J. London Math. Soc. 76: 2 (2007), 73–86.
   Web of Science ®Google Scholar
• [Castravet and Tevelev 06] A. M. Castravet and J. Tevelev. “Hilbert’s 14th Problem and Cox Rings.” Compos. Math. 142: 6 (2006), 1479–1498.
   Web of Science ®Google Scholar
• [Ciliberto 01] C. Ciliberto. “Geometrical Aspects of Polynomial Interpolation in More Variables and of Waring’s Problem.” In European Congress of Mathematics, Vol. I (Barcelona, 2000), edited by C. Casacuberta, R.M. Miro'-Roig, J. Verdera and S. Xambo'-Descamps. pp. 289–316, Progr. Math., 201. Basel: Birkhäuser, 2001
   Google Scholar
• [Ciliberto et al. 13] C. Ciliberto, B. Harbourne, R. Miranda, and J. Roé. “Variations on Nagata’s Conjecture.” Clay Math. Proc. 18 (2013) 185--203.
   Google Scholar
• [Ciliberto and Miranda, 98] C. Ciliberto and R. Miranda. “Degenerations of Planar Linear Systems.” J. Reine Angew. Math. 501 (1998), 191–220.
   Web of Science ®Google Scholar
• [Ciliberto and Russo 06] C. Ciliberto and F. Russo. “Varieties with Minimal Secant Degree and Linear Systems of Maximal Dimension on Surfaces.” Adv. Math. 200: 1 (2006), 1–50.
   Web of Science ®Google Scholar
• [Chandler 01] K. Chandler. “A Brief Proof of a Maximal Rank Theorem for Generic Double Points in Projective Space.” Trans. Am. Math. Soc. 353: 5 (2001), 1907–1920.
   Web of Science ®Google Scholar
• [Chandler 02] K. Chandler. “Linear Systems of Cubics Singular at General Points of Projective Space.” Compositio Mathematica 134 (2002), 269–282.
   Web of Science ®Google Scholar
• [Chandler 05] K. Chandler. “The Geometric Interpretation of Fröberg-Iarrobino conjectures on infinitesimal neighbourhoods of points in projective space.” J. Algebra 286: 2 (2005), 421–455.
   Web of Science ®Google Scholar
• [De Volder and Laface 07] C. De Volder and A. Laface. “On Linear Systems of Through Multiple Points.” J. Algebra 310: 1 (2007), 207–217.
   Web of Science ®Google Scholar
• [Dolgachev 83] I. Dolgachev. “Weyl Groups and Cremona Transformations.” Singularities, Summer Inst., Arcata/Calif. 1981, Proc. Sypm. Pure Math. 40, Part 1, 283--294 (1983).
   Google Scholar
• [Dumitrescu and Postinghel 14] O. Dumitrescu and E. Postinghel. “Vanishing Theorems for Linearly Obstructed Divisors.” arXiv:1403.6852 (2014).
   Google Scholar
• [Fröberg 85] R. Fröberg. “An Inequality for Hilbert Series of Graded Algebras.” Math. Scand. 56: 2 (1985), 117–144.
   Web of Science ®Google Scholar
• [Gimigliano 87] A. Gimigliano. “On Linear Systems of Plane Curves.” PhD diss., Queen’s University, Canada, 1987.
   Google Scholar
• [Harbourne 86] B. Harbourne. “The Geometry of Rational Surfaces and Hilbert Functions of Points in the Plane.” Can. Math. Soc. Conf. Proc. 6 (1986), 95–111.
   Google Scholar
• [Hirschowitz 89] A. Hirschowitz. “Une conjecture pour la cohomologie des diviseurs sur les surfaces rationnelles génériques.” J. Reine Angew. Math. 397 (1989), 208–213.
   Google Scholar
• [Hu and Keel 00] Y. Hu and S. Keel. “Mori Dream Spaces and GIT.” Michigan Math. J. 48 (2000), 331–348.
   Web of Science ®Google Scholar
• [Iarrobino 97] A. Iarrobino. “Inverse System of Symbolic Power III. Thin Algebras and Fat Points.” Compositio Math. 108: 3 (1997), 319–356.
   Web of Science ®Google Scholar
• [Laface and Ugaglia 06] A. Laface and L. Ugaglia. “On A Class of Special Linear Systems on .” Trans. Am. Math. Soc. 358: 12 (2006), 5485–5500 (electronic).
   Web of Science ®Google Scholar
• [Laface and Ugaglia 07] A. Laface and L. Ugaglia. “Elementary (−1) Curves of .” Commun. Algebra 35 (2007), 313–324.
   Web of Science ®Google Scholar
• [Mukai 04] S. Mukai. “Geometric Realization of T-Shaped Root Systems and Counterexamples to Hilbert’s Fourteenth Problem.” In Algebraic Transformation Groups and Algebraic Varieties Encyclopaedia of Mathematical Sciences Volume 132, pp. 123-129. 2004.
   Google Scholar
• [Mukai 05] S. Mukai. “Finite Generation of the Nagata Invariant Rings in A-D-E Cases.” RIMS Preprint 1502. 2005.
   Google Scholar
• [Postinghel 12] E. Postinghel. “A New Proof of the Alexander-Hirschowitz Interpolation Theorem.” Ann. Mat. Pura Appl. (4) 191: 1 (2012), 77–94.
   Web of Science ®Google Scholar
• [Sturmfels and Velasco 10] B. Sturmfels, M. Velasco. “Blow-ups of at n Points and Spinor Varieties.” J. Commut. Algebra 2: 2 (2010), 223–244.
   Web of Science ®Google Scholar
• [Sturmfels and Xu 10] B. Sturmfels and Z. Xu. “Sagbi Bases of Cox-Nagata Rings.” J. Eur. Math. Soc. (JEMS) 12: 2 (2010), 429–459.
   Web of Science ®Google Scholar
• [Veronese 81] G. Veronese. “Behandlung der projectivischen Verhältnisse der Räume von verschiedenen Dimensionen durch das Princip des Projicirens und Schneidens (German).” Math. Ann. 19: 2 (1881), 161–234.
   Google Scholar