Donu Arapura

Professor of Mathematics

• 765-49-41983

• MATH 642

arapura@purdue.edu
Personal Website

Research Interest(s):

algebraic geometry

Selected Publications

[1]	Donu Arapura. Lefschetz decompositions for eigenforms on a Kähler manifold. Proc. Amer. Math. Soc. , 146(5):2277--2281, 2018. [ bib | DOI | http ]
[2]	Donu Arapura. Simpson's construction of varieties with many local systems. In Hodge theory and L 2-analysis , volume 39 of Adv. Lect. Math. (ALM) , pages 79--86. Int. Press, Somerville, MA, 2017. [ bib ]
[3]	Donu Arapura. Toward the structure of fibered fundamental groups of projective varieties. J. Éc. polytech. Math. , 4:595--611, 2017. [ bib | DOI | http ]
[4]	Donu Arapura, Alexandru Dimca, and Richard Hain. On the fundamental groups of normal varieties. Commun. Contemp. Math. , 18(4):1550065, 17, 2016. [ bib | DOI | http ]
[5]	Donu Arapura. Geometric Hodge structures with prescribed Hodge numbers. In Recent advances in Hodge theory , volume 427 of London Math. Soc. Lecture Note Ser. , pages 414--421. Cambridge Univ. Press, Cambridge, 2016. [ bib ]
[6]	Donu Arapura. Differential forms: theory and practice . Second edition. [book review of MR3319041]. SIAM Rev. , 57(4):630--632, 2015. [ bib ]
[7]	Donu Arapura. Restrictions on the prime-to- p fundamental group of a smooth projective variety. Compos. Math. , 151(6):1083--1095, 2015. [ bib | DOI | http ]
[8]	Donu Arapura. Decomposition of direct images of logarithmic differentials. Int. Math. Res. Not. IMRN , (3):763--772, 2015. [ bib | DOI | http ]
[9]	Donu Arapura, Xi Chen, and Su-Jeong Kang. The smooth center of the cohomology of a singular variety. In Hodge theory, complex geometry, and representation theory , volume 608 of Contemp. Math. , pages 1--19. Amer. Math. Soc., Providence, RI, 2014. [ bib | DOI | http ]
[10]	Donu Arapura. Hodge theory of cyclic covers branched over a union of hyperplanes. Canad. J. Math. , 66(3):505--524, 2014. [ bib | DOI | http ]
[11]	Donu Arapura, Parsa Bakhtary, and Jarosl aw Wl odarczyk. Weights on cohomology, invariants of singularities, and dual complexes. Math. Ann. , 357(2):513--550, 2013. [ bib | DOI | http ]
[12]	Donu Arapura. An abelian category of motivic sheaves. Adv. Math. , 233:135--195, 2013. [ bib | DOI | http ]
[13]	Donu Arapura. Algebraic geometry over the complex numbers . Universitext. Springer, New York, 2012. [ bib | DOI | http ]
[14]	Donu Arapura. Frobenius amplitude, ultraproducts, and vanishing on singular spaces. Illinois J. Math. , 55(4):1367--1384 (2013), 2011. [ bib | http ]
[15]	Donu Arapura and Su-Jeong Kang. Kähler-de Rham cohomology and Chern classes. Comm. Algebra , 39(4):1153--1167, 2011. [ bib | DOI | http ]
[16]	Donu Arapura. Homomorphisms between Kähler groups. In Topology of algebraic varieties and singularities , volume 538 of Contemp. Math. , pages 95--111. Amer. Math. Soc., Providence, RI, 2011. [ bib | DOI | http ]
[17]	Donu Arapura. Mixed Hodge structures associated to geometric variations. In Cycles, motives and Shimura varieties , volume 21 of Tata Inst. Fund. Res. Stud. Math. , pages 1--34. Tata Inst. Fund. Res., Mumbai, 2010. [ bib ]
[18]	Donu Arapura. The Hodge theoretic fundamental group and its cohomology. In The geometry of algebraic cycles , volume 9 of Clay Math. Proc. , pages 3--22. Amer. Math. Soc., Providence, RI, 2010. [ bib ]
[19]	Donu Arapura. Varieties with very little transcendental cohomology. In Motives and algebraic cycles , volume 56 of Fields Inst. Commun. , pages 1--14. Amer. Math. Soc., Providence, RI, 2009. [ bib ]
[20]	Donu Arapura and Manish Kumar. Beilinson-Hodge cycles on semiabelian varieties. Math. Res. Lett. , 16(4):557--562, 2009. [ bib | DOI | http ]
[21]	Donu Arapura and Ajneet Dhillon. The motive of the moduli stack of G -bundles over the universal curve. Proc. Indian Acad. Sci. Math. Sci. , 118(3):389--411, 2008. [ bib | DOI | http ]
[22]	Donu Arapura and Su-Jeong Kang. Functoriality of the coniveau filtration. Canad. Math. Bull. , 50(2):161--171, 2007. [ bib | DOI | http ]
[23]	Donu Arapura and Su-Jeong Kang. Coniveau and the Grothendieck group of varieties. Michigan Math. J. , 54(3):611--622, 2006. [ bib | DOI | http ]
[24]	Donu Arapura. Motivation for Hodge cycles. Adv. Math. , 207(2):762--781, 2006. [ bib | DOI | http ]
[25]	Donu Arapura. Partial regularity and amplitude. Amer. J. Math. , 128(4):1025--1056, 2006. [ bib | .pdf ]
[26]	Donu Arapura. The Leray spectral sequence is motivic. Invent. Math. , 160(3):567--589, 2005. [ bib | DOI | http ]
[27]	Donu Arapura and Chris Peterson. The common invariant subspace problem: an approach via Gröbner bases. Linear Algebra Appl. , 384:1--7, 2004. [ bib | DOI | http ]
[28]	Donu Arapura. Kähler solvmanifolds. Int. Math. Res. Not. , (3):131--137, 2004. [ bib | DOI | http ]
[29]	Donu Arapura. Frobenius amplitude and strong vanishing theorems for vector bundles. Duke Math. J. , 121(2):231--267, 2004. With an appendix by Dennis S. Keeler. [ bib | DOI | http ]
[30]	Donu Arapura and Sviatoslav Archava. Kodaira dimension of symmetric powers. Proc. Amer. Math. Soc. , 131(5):1369--1372, 2003. [ bib | DOI | http ]
[31]	Donu Arapura. Higgs bundles, integrability, and holomorphic forms. In Motives, polylogarithms and Hodge theory, Part II (Irvine, CA, 1998) , volume 3 of Int. Press Lect. Ser. , pages 605--624. Int. Press, Somerville, MA, 2002. [ bib ]
[32]	Donu Arapura. A class of sheaves satisfying Kodaira's vanishing theorem. Math. Ann. , 318(2):235--253, 2000. [ bib | DOI | http ]
[33]	Donu Arapura and Pramathanath Sastry. Intermediate Jacobians and Hodge structures of moduli spaces. Proc. Indian Acad. Sci. Math. Sci. , 110(1):1--26, 2000. [ bib | DOI | http ]
[34]	Donu Arapura. Building mixed Hodge structures. In The arithmetic and geometry of algebraic cycles (Banff, AB, 1998) , volume 24 of CRM Proc. Lecture Notes , pages 13--32. Amer. Math. Soc., Providence, RI, 2000. [ bib ]
[35]	Donu Arapura and Madhav Nori. Solvable fundamental groups of algebraic varieties and Kähler manifolds. Compositio Math. , 116(2):173--188, 1999. [ bib | DOI | http ]
[36]	Donu Arapura and Kyungho Oh. On the Abel-Jacobi map for non-compact varieties. Osaka J. Math. , 34(4):769--781, 1997. [ bib | http ]
[37]	Donu Arapura. Geometry of cohomology support loci for local systems. I. J. Algebraic Geom. , 6(3):563--597, 1997. [ bib ]
[38]	Donu Arapura. Fundamental groups of smooth projective varieties. In Current topics in complex algebraic geometry (Berkeley, CA, 1992/93) , volume 28 of Math. Sci. Res. Inst. Publ. , pages 1--16. Cambridge Univ. Press, Cambridge, 1995. [ bib | DOI | http ]
[39]	Donu Arapura and Kyungho Oh. Abel's theorem for twisted Jacobians. Trans. Amer. Math. Soc. , 342(1):421--433, 1994. [ bib | DOI | http ]
[40]	D. Arapura, P. Bressler, and M. Ramachandran. On the fundamental group of a compact Kähler manifold. Duke Math. J. , 68(3):477--488, 1992. [ bib | DOI | http ]
[41]	Donu Arapura. Higgs line bundles, Green-Lazarsfeld sets, and maps of Kähler manifolds to curves. Bull. Amer. Math. Soc. (N.S.) , 26(2):310--314, 1992. [ bib | DOI | http ]
[42]	Donu Arapura. Fano maps and fundamental groups. In Algebraic geometry (Chicago, IL, 1989) , volume 1479 of Lecture Notes in Math. , pages 10--14. Springer, Berlin, 1991. [ bib | DOI | http ]
[43]	Donu Arapura. Hodge theory with local coefficients on compact varieties. Duke Math. J. , 61(2):531--543, 1990. [ bib | DOI | http ]
[44]	Donu Arapura. Local cohomology of sheaves of differential forms and Hodge theory. J. Reine Angew. Math. , 409:172--179, 1990. [ bib | DOI | http ]
[45]	Donu Arapura. A short proof of Rohlin's theorem for complex surfaces. Proc. Amer. Math. Soc. , 108(4):1143--1144, 1990. [ bib | DOI | http ]
[46]	Donu Arapura. Smoothable varieties with torsion free canonical sheaf. Manuscripta Math. , 63(1):17--20, 1989. [ bib | DOI | http ]
[47]	Donu Arapura. Hodge theory with local coefficients and fundamental groups of varieties. Bull. Amer. Math. Soc. (N.S.) , 20(2):169--172, 1989. [ bib | DOI | http ]
[48]	Donu Arapura and David B. Jaffe. On Kodaira vanishing for singular varieties. Proc. Amer. Math. Soc. , 105(4):911--916, 1989. [ bib | DOI | http ]
[49]	Donu Arapura. Vanishing theorems for V -manifolds. Proc. Amer. Math. Soc. , 102(1):43--48, 1988. [ bib | DOI | http ]
[50]	Donu Arapura. A note on Kollár's theorem. Duke Math. J. , 53(4):1125--1130, 1986. [ bib | DOI | http ]