Alexandru Dimca

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Questions related from Alexandru Dimca

Is the SL_2-orbit of $x^4y^2$ in the closure of the SL_2-orbit of x^6+y^6 ?

We consider the 6-dimensional complex projective space of non-zero binary sextic forms in x and y. Then the group $SL_2(C)$ acts here by change of coordinates. Hence any binary form has a...

07 August 2022 3,509 3 View

Does any smooth surface S in P^3 admit a plane section which is a free curve ?

If the degree of S is 2, then take H a tangent plane, and the corresponding section is free. When the degree of S is 3, then take H a tritangent plane, and the corresponding section is free. First...

18 January 2022 8,869 5 View

When two given plane curves are projectively equivalent ?

Consider the following two smooth projective, complex plane curves C: x^d+y^d+z^d+(ax+by+cz)^d=0 and C': x^d+y^d+z^d+(a'x+b'y)^d=0 where a,b,c,a',b' are small nonzero complex numbers. Can you...

31 March 2020 6,044 4 View

If S is a polynomial ring in k variables, and M is a graded S-submodule in S^n, when does one know a bound on the minimal number of generators for M?

One may suppose that M is the kernel of a morphism S^n to S^m of free S-modules, and that S is a polynomial ring in x_1,...,x_k with complex coefficients.

01 January 1970 4,386 6 View