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There are following sources on the Griffiths infinitesimal invariant.

Original ideas of Griffiths are contained here (1983):

[1] MR0720288 (86e:32026a)  Carlson, James;  Green, Mark;  Griffiths, Phillip; Harris, Joe. Infinitesimal variations of Hodge structure. I. Compositio Math.  50  (1983),  no. 2-3, 109--205.

[2] MR0720289 (86e:32026b)  Griffiths, Phillip;  Harris, Joe. Infinitesimal variations of Hodge structure. II. An infinitesimal invariant of Hodge classes. Compositio Math.  50  (1983),  no. 2-3, 207--265.

[3] MR0720290 (86e:32026c)  Griffiths, Phillip A.  Infinitesimal variations of Hodge structure. III. Determinantal varieties and the infinitesimal invariant of normal functions. Compositio Math.  50  (1983),  no. 2-3, 267--324.

Then goes a paper by Green (1989):

[4] MR0992330 (90c:14006)  Green, Mark L.  Griffiths' infinitesimal invariant and the Abel-Jacobi map. J. Differential Geom.  29  (1989),  no. 3, 545--555.

Expository papers of Green and Voisin (1994):

[5] MR1335239 (96m:14012)  Green, Mark L.  Infinitesimal methods in Hodge theory. Algebraic cycles and Hodge theory (Torino, 1993),  1--92, Lecture Notes in Math., 1594, Springer, Berlin,  1994.

[6] MR1335241 (96i:14007)  Voisin, Claire. Transcendental methods in the study of algebraic cycles. Algebraic cycles and Hodge theory (Torino, 1993),  153--222, Lecture Notes in Math., 1594, Springer, Berlin,  1994.

A book by Voisin on Hodge theory (2002-2003):

[7] MR1967689 (2004d:32020)  Voisin, Claire. Hodge theory and complex algebraic geometry. I. Translated from the French original by Leila Schneps. Cambridge Studies in Advanced Mathematics, 76. Cambridge University Press, Cambridge,  2002. x+322 pp. ISBN: 0-521-80260-1

[8] MR1997577 (2005c:32024b)  Voisin, Claire. Hodge theory and complex algebraic geometry. II. Translated from the French by Leila Schneps. Cambridge Studies in Advanced Mathematics, 77. Cambridge University Press, Cambridge,  2003. x+351 pp. ISBN: 0-521-80283-0

A survey paper by Griffiths (2004):

[9] MR2083750 (2005g:14023)  Griffiths, Phillip. Hodge theory and geometry. Bull. London Math. Soc.  36  (2004),  no. 6, 721--757.

The papers that seemed interesting:

[10] MR1625958 (99i:14010)  Westhoff, Randall F.  Computing the infinitesimal invariants associated to deformations of subvarieties. Pacific J. Math.  183  (1998),  no. 2, 375--397.

[11] MR1487220 (98m:14010)  Collino, A.  Griffiths' infinitesimal invariant and higher $K$-theory on hyperelliptic Jacobians. J. Algebraic Geom.  6  (1997),  no. 3, 393--415.

[12] MR1162437 (93f:14004)  Muller-Stach, Stefan. On the nontriviality of the Griffiths group. J. Reine Angew. Math.  427  (1992), 209--218.

[13] MR2061847 (2005e:14014)  Muller-Stach, Stefan ;  Saito, Shuji ;  Collino, A.  On $K\sb 1$ and $K\sb 2$ of algebraic surfaces. Special issue in honor of Hyman Bass on his seventieth birthday. Part I. $K$-Theory  30  (2003),  no. 1, 37--69.

Something related to Manin's example:

[14] MR1732409 (2001b:14086)  Manin, Yu. I.  Sixth Painleve equation, universal elliptic curve, and mirror of $\bold P\sp 2$. Geometry of differential equations,  131--151, Amer. Math. Soc. Transl. Ser. 2, 186, Amer. Math. Soc., Providence, RI,  1998.

[15] MR1896474 (2003g:14007)  del Angel, Pedro Luis;  Muller-Stach, Stefan J.  The transcendental part of the regulator map for $K\sb 1$ on a mirror family of $K3$-surfaces. Duke Math. J.  112  (2002),  no. 3, 581--598.

[16] MR2019146 (2005b:14018)  del Angel, Pedro Luis;  Muller-Stach, Stefan. Picard-Fuchs equations, integrable systems and higher algebraic $K$-theory. Calabi-Yau varieties and mirror symmetry (Toronto, ON, 2001), 43--55, Fields Inst. Commun., 38, Amer. Math. Soc., Providence, RI,  2003.

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