I am professor at the Departamento de Álgebra of the Facultad
de Matemáticas
of the Universidad Complutense de Madrid.
My field of research is Algebraic Geometry. I work on this topics:



I am part of the research group Geometría de las
variedades proyectivas and the Instituto de Matemática
Interdisciplinar (IMI), of the Universidad Complutense
de Madrid.



Publication list.

F.J. Gallego, L. Giraldo, and I. Sols, "Bounding families of ruled surfaces",

Proc. Amer. Math. Soc. 124 (1996), 2943-2951.


F.J. Gallego and B.P. Purnaprajna, "Normal presentation on elliptic ruled surfaces",

J. Algebra 186 (1996), 597-625.


F.J. Gallego and B.P. Purnaprajna, "Higher syzygies of elliptic ruled surfaces",

J. Algebra 186 (1996), 626-659.


F.J. Gallego and B.P. Purnaprajna, "Degenerations of K3 surfaces in projective

space", Trans. Amer. Math. Soc. 349 (1997), 2477-2492.


F.J. Gallego, and B.P. Purnaprajna, "Very ampleness and higher syzygies for

Calabi-Yau threefolds", Math. Ann. 312 (1998), 133-149.


F.J. Gallego and B.P. Purnaprajna, "Projective normality and syzygies of algebraic

surfaces", J. Reine Angew. Math. 506 (1999), 145- 180.

Erratum,   J. Reine Angew. Math. 523 (2000), 233-234.


F.J. Gallego and B.P. Purnaprajna, "Syzygies of projective surfaces: an overview",

J. Ramanujan Math. Soc. 14 (1999), 65-93.


F.J. Gallego and B.P. Purnaprajna, "Vanishing theorems and syzygies for K3

surfaces and Fano varieties", J. Pure Appl. Algebra 146 (2000), 251-265.


F.J. Gallego and B.P. Purnaprajna, "Some results on rational surfaces and Fano

varieties", J. Reine Angew. Math. 538 (2001), 25-55.


F.J. Gallego and B.P. Purnaprajna, "On the canonical ring of covers of surfaces of

minimal degree", Trans. Amer. Math. Soc. 355 (2003), 2715-2732.


F.J. Gallego and B.P. Purnaprajna, "Some homogeneous rings associated to finite

morphisms", Advances In Algebra and Geometry (Hyderabad 2001), 159-169,

Hindustan Book Agency, New Delhi, 2003.



F.J. Gallego and B.P. Purnaprajna, "Triple canonical covers of varieties of minimal

degree", A Tribute to C.S. Seshadri. Perspectives in Geometry and Representation

Theory (Chennai, 2002), 241-270, Trends Math., Birkhaüser, Basel, 2003.



F.J. Gallego and B.P. Purnaprajna, "Classification of quadruple canonical covers:

Galois case", C. R. Math. Acad. Sci. Soc. R. Can. 26 (2004), 45-50.


F.J. Gallego and B.P. Purnaprajna, "Classification of quadruple Galois canonical

covers, II", J. Algebra 312 (2007), 798-828.


F.J. Gallego and B.P. Purnaprajna, "Classification of quadruple Galois canonical

covers, I", Trans. Amer. Math. Soc. 360 (2008), 5489-5507.


F.J. Gallego, M. González and B.P. Purnaprajna, "K3 double structures on Enriques

surfaces and their smoothings", J. Pure Appl. Algebra 212 (2008), 981-993.


F.J. Gallego, M. González and B.P. Purnaprajna, "Deformation of finite morphisms and

smoothings of ropes'', Compositio Math. 144 (2008), 673-688.



F.J. Gallego, M. González  and B.P. Purnaprajna,
"Deformation of canonical morphisms

and the moduli of surfaces of general type” , Invent. Math. 182 (2010), 1-46.


F.J. Gallego and B.P. Purnaprajna,  On the bicanonical morphism of quadruple Galois

canonical covers, Trans. Amer. Math. Soc.  363 (2011), 4401-4420.


F.J. Gallego, M. González and B.P. Purnaprajna, "An infinitesimal condition to smooth ropes”

Revista Matemática Complutense 26 (2013), 253-269.


F.J. Gallego, M. González and B.P. Purnaprajna,  "Canonical double covers of minimal rational

surfaces and the non-existence of carpets”, J. Algebra 374 (2013), 231-244.


F.J. Gallego, M. González and B.P. Purnaprajna, "Deformations of bicanonical morphisms of

genus-2 fibrations”, Proc. CAAG 2010, RMS-Lecture Notes Series 17 (2013), 1-12.


F.J. Gallego, M. González and B.P. Purnaprajna,  "Smoothable locally non Cohen–Macaulay

double structures on curves", Collect. Math.  65 (2014), 417-433.


F.J. Gallego, M. González and B.P. Purnaprajna,  "Deformations of canonical double covers”,

J. Algebra 463 (2016), 1-9.


F.J. Gallego, M. González and B.P. Purnaprajna,  "Deformations of canonical triple covers”,

J. Algebra 463 (2016), 23-32.