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Dr. Donu Arapura

Dr. 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. [
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[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. [
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[4] Donu Arapura, Alexandru Dimca, and Richard Hain. On the fundamental groups of normal varieties.
Commun. Contemp. Math.
, 18(4):1550065, 17, 2016. [
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[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. [
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[8] Donu Arapura. Decomposition of direct images of logarithmic differentials.
Int. Math. Res. Not. IMRN
, (3):763--772, 2015. [
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[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. [
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[10] Donu Arapura. Hodge theory of cyclic covers branched over a union of hyperplanes.
Canad. J. Math.
, 66(3):505--524, 2014. [
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[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. [
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[12] Donu Arapura. An abelian category of motivic sheaves.
Adv. Math.
, 233:135--195, 2013. [
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[13] Donu Arapura.
Algebraic geometry over the complex numbers
. Universitext. Springer, New York, 2012. [
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[14] Donu Arapura. Frobenius amplitude, ultraproducts, and vanishing on singular spaces.
Illinois J. Math.
, 55(4):1367--1384 (2013), 2011. [
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[15] Donu Arapura and Su-Jeong Kang. Kähler-de Rham cohomology and Chern classes.
Comm. Algebra
, 39(4):1153--1167, 2011. [
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[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
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]
[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. [
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[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. [
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[22] Donu Arapura and Su-Jeong Kang. Functoriality of the coniveau filtration.
Canad. Math. Bull.
, 50(2):161--171, 2007. [
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[23] Donu Arapura and Su-Jeong Kang. Coniveau and the Grothendieck group of varieties.
Michigan Math. J.
, 54(3):611--622, 2006. [
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[24] Donu Arapura. Motivation for Hodge cycles.
Adv. Math.
, 207(2):762--781, 2006. [
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[25] Donu Arapura. Partial regularity and amplitude.
Amer. J. Math.
, 128(4):1025--1056, 2006. [
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.pdf
]
[26] Donu Arapura. The Leray spectral sequence is motivic.
Invent. Math.
, 160(3):567--589, 2005. [
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[27] Donu Arapura and Chris Peterson. The common invariant subspace problem: an approach via Gröbner bases.
Linear Algebra Appl.
, 384:1--7, 2004. [
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[28] Donu Arapura. Kähler solvmanifolds.
Int. Math. Res. Not.
, (3):131--137, 2004. [
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[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. [
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[30] Donu Arapura and Sviatoslav Archava. Kodaira dimension of symmetric powers.
Proc. Amer. Math. Soc.
, 131(5):1369--1372, 2003. [
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[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. [
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[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. [
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[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. [
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[36] Donu Arapura and Kyungho Oh. On the Abel-Jacobi map for non-compact varieties.
Osaka J. Math.
, 34(4):769--781, 1997. [
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[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. [
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[39] Donu Arapura and Kyungho Oh. Abel's theorem for twisted Jacobians.
Trans. Amer. Math. Soc.
, 342(1):421--433, 1994. [
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[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. [
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[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. [
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[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. [
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[43] Donu Arapura. Hodge theory with local coefficients on compact varieties.
Duke Math. J.
, 61(2):531--543, 1990. [
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[44] Donu Arapura. Local cohomology of sheaves of differential forms and Hodge theory.
J. Reine Angew. Math.
, 409:172--179, 1990. [
bib
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[45] Donu Arapura. A short proof of Rohlin's theorem for complex surfaces.
Proc. Amer. Math. Soc.
, 108(4):1143--1144, 1990. [
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[46] Donu Arapura. Smoothable varieties with torsion free canonical sheaf.
Manuscripta Math.
, 63(1):17--20, 1989. [
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[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
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[48] Donu Arapura and David B. Jaffe. On Kodaira vanishing for singular varieties.
Proc. Amer. Math. Soc.
, 105(4):911--916, 1989. [
bib
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[49] Donu Arapura. Vanishing theorems for
V
-manifolds.
Proc. Amer. Math. Soc.
, 102(1):43--48, 1988. [
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[50] Donu Arapura. A note on Kollár's theorem.
Duke Math. J.
, 53(4):1125--1130, 1986. [
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