Francesc Planas Vilanova homepage
Francesc Planas Vilanova
Publications
-
Binomial determinants: some closed formulae
(with Laura González)
Preprint in
arXiv:2603.29431
- Prime ideals of Moh
and the characteristic of the field (with Laura González)
J. Algebra Appl.
doi:10.1142/S0219498827501702
- Elements with
unique length factorization of a numerical semigroup generated by
three consecutive numbers (with Pedro
A. García-Sánchez and Laura González)
Semigroup Forum
112 (2026), 79–105.
-
Sifted degrees of the equations of the Rees module and their
connection with the Artin-Rees numbers (with Philippe Gimenez)
Commutative Algebra. The Mathematical Legacy of Wolmer V. Vasconcelos.
De Gruyter (2025), 333-352.
-
Regular local rings of dimension four and
Gorenstein syzygetic prime ideals
J. Algebra 601 (2022), 105–114.
-
Divisors of expected Jacobian type
(with Josep Àlvarez Montaner)
Math. Scand. 127 (2021), no. 2, 161–184.
-
Noetherian rings of low global dimension and syzygetic prime ideals
J. Pure Appl. Algebra 225 (2021), no. 2, 106494.
- On the integral
degree of integral ring extensions
(with José M. Giral, Liam O'Carroll and Bernat Plans)
Proc. Edinb. Math. Soc.
62 (2019), 25-46.
- Minimal free resolutions
of lattice ideals of digraphs
(with Liam O'Carroll)
Algebraic Combinatorics 1 (2018), 283-326.
- The relation type of
affine algebras and algebraic varieties
J. Algebra 441 (2015), 166-179.
- Non-complete
intersection prime ideals in dimension 3
(with Shiro Goto and Liam O'Carroll)
Kyoto
J. Math. 55 (2015), 461-475.
- Degree and algebraic
properties of lattice and binomial matrix ideals
(with Liam O'Carroll and Rafael H.Villarreal)
SIAM J. Discrete
Math. 28 (2014), 394-427.
- J. Sally's question
and a conjecture of Y. Shimoda
(with Shiro Goto and Liam O'Carroll)
Nagoya Math. J. 211 (2013), 137-161.
-
The equations of Rees algebras of equimultiple ideals of
deviation one (with Ferran Muiños)
Proc. Amer. Math. Soc. 141 (2013), 1241-1254.
- The primary components of
positive critical binomial ideals
(with Liam O'Carroll)
J. Algebra 373 (2013), 392-413.
- Ideals of
Herzog-Northcott type
(with Liam O'Carroll)
Proc. Edinb. Math. Soc.
54 (2011), 161-186.
-
On the ring of global sections of the blowing-up along a
two-generated ideal (with José M. Giral)
J. Pure Appl. Algebra 213 (2009), 601-604.
-
On the injectivity of blowing-up ring morphisms (with
Ferran Muiños)
J. Algebra 320 (2008), 3365-3380.
-
Irreducible affine space curves and the uniform Artin-Rees property on
the prime spectrum (with Liam O'Carroll)
J. Algebra 320 (2008), 3339-3344.
-
Integral degree of a ring, reduction numbers and uniform
Artin-Rees numbers (with José M. Giral)
J. Algebra 319 (2008), 3398-3418.
-
A note on the acyclicity of the Koszul complex of a module
(with José M. Giral)
Ark. Mat. 45 (2007), 273-278.
-
An approach to the uniform Artin-Rees theorems from the notion
of relation type
Commutative algebra.
Geometric, homological, combinatorial and computational aspects.
Lecture Notes in Pure and Applied Mathematics, 244 (2006), 175-191.
-
Normal transversality and uniform bounds
J. Lond. Math. Soc. (2)
62 (2000), 716-728.
-
The strong uniform Artin-Rees property in codimension one
J. reine
angew. Math. 527 (2000), 185-201.
-
On the module of effective relations of a standard algebra
Math.
Proc. Cambridge Philos. Soc. 124 (1998), 215-229.
-
On the vanishing and non-rigidity of the André-Quillen
(co)homology
J. Pure Appl. Algebra 120 (1997), 67-75.
-
Rings of weak dimension one and syzygetic ideals
Proc. Amer. Math. Soc. 124 (1996),
3015-3017.
-
Vanishing of the André-Quillen homology module $H_{2}(A,B,G(I))$
Comm. Algebra 24 (1996), 2777-2791.
-
Sur l'annulation du deuxième foncteur de (co)homologie
d'André-Quillen
Manuscripta Math. 87 (1995), 349-357.