# Preprints, Shigeru MUKAI

RIMS preprint (2001-)
• #1343: Conterexample to Hilbert's fourteenth problem for the 3-dimensional additive group, 2001
• #1372: Geometric realization of T-Shaped root systems and counterexamples to Hilbert's fourteenth problem, 2002. (Algebraic Transformation Group and Algebraic Varieties, pp.120-130, Springer Verlag, Berlin, 2004)
• #1395: Curves and symmetric spaces, II, 2003. (Ann. of Math. 172(2010), 1539-1558.)
• #1403: Canonical curves of genus eight, 2003 (with Manabu IDE, Proc. Japan Acad. 79(2003), 59-64)
• #1422: Plane quartics and Fano threefolds of genus twelve, 2003. (The Fano Conference, pp.563-572, 2004, Univ. Torino)
• #1502: Finite generation of the Nagata invariant rings in A-D-E cases, 2005.
• #1505: Counterexample of Kodaira's vanishing and Yau's ineqauality in higher dimensional variety of characteristic p>0, 2005. (Originally typeset around 1980.)
• #1544: Numerically trivial involutions of Enriques surfaces, May 2006. (One type was omitted in the classification in 1984.) (Kyoto J. Math. 50(2010), no. 4, 889-902.) KURI-Repository
• #1562: (with H. Nasu) Obstructions to deforming curves on a 3-fold, I --- a generalization of Mumford's example and an application to Hom schemes ---, July 2006. ( Journal of Algebraic Geometry, 18(2009), no. 4, 691-709.)
• #1633: Kummer's quartics and numerically reflective involutions of Enriques surfaces, June 2008. (Conjecture 3 has been solved by H. Ohashi in his recent preprint "Enriques surfaces covered by Jacobian Kummer surfaces".) (J. Math. Soc. Japan. 64(2012), 231-246.) KURI-Repository
• Addendum to #1544: Addendum to "Numerically trivial involutions of Enriques surfaces", October 2009. (Involutions of Lieberman type are not cohomologically trivial.)
• #1736: Counterexamples of Kodaira's vanishing and Yau's inequality in positive characteristics, 2011. (Revised English translation of "On counterexamples of Kodaira's vanishing and Yau's inequality in positive characteristics (in Japanese), Proceeding of Kinosaki algebraic geometry symposium, 1979, pp. 9--31.) KURI-Repository
• #1743 : K3 surfaces of genus sixteen, February 2012. "Minimal models and extremal rays", Adv. Stud. Pure Math. 70, Math. Soc. Japan, Tokyo, 2016, pp. 379--396. genus16.pdf

Abstract. The generic polarized $K3$ surface (S, h) of genus 16, that is, (h^2)=30, is described in a certain compactifeid moduli space \mathcal{T} of twisted cubics in P^3, as a com plete intersection with respect to an almost homogeneous vector bundle of rank 10. As corollary we prove the unirationality of the moduli space \mathcal{F}_{16} of such K3 surfaces.

• #1751 : (with H. Ohashi) Enriques surfaces of Hutchinson-Gopel type and Mathieu automorphism, June 2012. ("Arithmetic and Geometry of K3 surfaces and Calabi-Yau Threefoolds", eds. M. Schuett, R. Laza and N. Yui, Fields Inst. for Research in Math. Sciences, Springer-Verlag, 2013)
• #1795 : (with H. Ohashi) The automorphism groups of Enriques surfaces covered by symmetric quartic surfaces, February 2014. In Recent Advances in Algebraic Geometry", A volume in honor of Rob Lazarsfeld's 60th birthday, eds. Hacon, Mustata and Popa, Cambridge Univ. Press, 2015, 307--320. KURI-Repository
• #1961 : Curves and symmetric spaces III: BN-special vs. 1-PS degeneration, June 2022. Proc. Indian Acad. Sci. (Math. Sci.), 132:57(2022). Special issue in Memory of Prof. C.S. Seshadri.

• INI preprint (Programme: Moduli spaces MOS) NI11008-MOS: Igusa quartic and Steiner surfaces, Contemp. Math. 564(2012), 205-210. Igusa-Steiner.pdf
• Correction published in "Siegel modular forms of genus 2 and level 2" by F. Clery, G. van der Geer and S. Grushevsky (Int. J. Math., 26(2015)) as an appendix. IQSS_correction.pdf