Chiara Mastroianni: Independent woman

There's no escaping Chiara Mastroianni's genes. The daughter of two of European cinema's most beloved icons - Catherine Deneuve and Marcello Mastroianni - looks as fabulous as you would expect. Her face is a curious composite of her parents': her mother's bone structure married to the softer, lazier features of her father. The effect is unquestionably beautiful, but Mastroianni wears it casually. Such lineage must be a hard act to follow.

Now 32, she has been acting for some time. Her career to date has been low-key, characterised by small parts in interesting projects such as Robert Altman's Prêt à Porter, Raoul Ruiz's Time Regained and Mike Figgis's Hotel. Her latest performance, in Delphine Gleize's debut feature, Carnages, is similarly offbeat. The role gives her the chance to show her quirky, comedic side, and provides evidence that Mastroianni picked up more than good looks from her parents. In the film, she plays Carlotta, a struggling actress fast losing sight of her own identity. She attends rebirthing workshops, standing naked among strangers in a swimming-pool while trying to find her inner scream. Her character desires change that goes beyond the psychological: she's in the process of having moles sliced from her skin.

Like much of Mastroianni's work, Carnages is an ensemble piece. It interweaves a clutch of disparate characters all connected by the remains of a bull killed in the ring - Carlotta finds herself dressed in a flamenco costume as part of a supermarket promotion to flog the beast's skeleton to dog-owners. Gleize's eye is at once cinematic, earthy and surreal - Carnages is unlike any film you've seen.

"The script made sense to me," Mastroianni shrugs when I ask what drew her to such an unusual project. "Sure, there are a lot of characters all living their own stories, but I have read many more conventional scripts that I had to reread because I completely lost the point. Carnages just made sense."

Alongside the clarity of the writing, Mastroianni also welcomed the chance to play such a fanciful character. "Most of the parts I'd been offered were straightforward people with a dark side," she says. "Carlotta has a craziness about her that is both bizarre and disturbing - and often funny."

Despite being attracted by Carlotta's humour, Mastroianni also found that facet of her personality daunting. "It was scary," she admits with a giggle. "The rhythm of comedy is so different - it was easy to make her crazy, but to make her funny as well was hard. Carlotta is not quite finished. She has some way to go to become formed. She doesn't really know who she is and she is searching - I think that she is really just a child. I mean, having her moles cut off to be rid of her parents? She doesn't want to be reminded of them, but they are written all over her."

The fact that Mastroianni's skin is speckled with moles is a coincidence, and she insists that the part was not written with her in mind. She admits that her close physical similarity to her character made the role uncomfortable to play, having also gone through periods of wanting rid of her visible imperfections. She starts to laugh. "My mole trauma stems from a different place. All children hate them - they point and say things like: 'You've got chocolate on your face.' When I was a child, and as a teenager, I was ashamed of my skin. I saw many doctors about the possibility of getting rid of them but I never actually took the step to have the surgery."

How does she feel about them now? "Oh," she smiles, "we've reached a peaceful cohabitation. I think that although I felt physically different because of them, I knew deep down that they were a part of my identity."

Mastroianni married the French electronica musician Benjamin Biolay three years ago, and the couple have a 10-month-old daughter, Anna. Chiara also has a seven-year-old son, Milo, from a previous relationship, but still found being pregnant for the second time, with Anna, a difficult experience. "It's supposed to be so natural," she sighs, "and you're supposed to know what is going on, yet it can feel so strange having this life inside you."

After Carnages, there are no new acting projects on the horizon. She has, however, been diversifying, "singing and writing a little" on a record under the band name Home. "It started off at home, more like a game," she tells me, a sense of excitement in her voice. "And now we are going to release an album in April." She giggles when I ask her if this is a calculated career move. "I really didn't think of it that way - it was just something that I found both strange and interesting to do."

Mastroianni shrugs off the notion that music might become a significant part of her life. For the moment, domestic responsibilities are her priority, and the birth of Anna has given her time to ruminate further on the parent-child bond.

"In Carnages, Carlotta is always talking about not being a part of your parents because you are your own person, but this is a bit skewed," she suggests. "I know that the bond with your parents is very complicated and I'm in the process of working that out with my son. You want to be yourself and yet you are from your parents and nothing can change that."

This statement brings us neatly round to where we began. I ask her how she feels when interviewers look at her and see only her parents. The question furrows her beautiful brow. "Any film I am in, if the character says anything about their father, all the journalists ask me if this is how I feel about my father. It's as if they think I've written the script, or I look for characters that are about me."

Mastroianni's famous lineage has caused her to adopt diversionary tactics to maintain her privacy. "I've reached a point where I have a few tried and tested things that I say," she admits. "It may make me sound cynical, but I find that any little thing I might share is overanalysed. If I said, for example - and I'm only saying this as an example - that I used to go skiing with my father, then the picture drawn is not of a little girl holidaying with her dad, but of 'oh, the famous Italian actor used to ski'. But if you told me something about your parents," she smiles, "I would only listen to what you were saying, and that would be what the conversation was about."

"It's sad really," she adds quietly. "Because I think that if my parents were more anonymous, then I would share more. But I don't want to be overanalysed, so instead I choose to protect myself."

Don't treat me like a child: Celebrity offspring on their famous mums and dads

SOFIA COPPOLA

The director of Lost in Translation, Sofia Coppola, 33, is the daughter of the movie director Francis Ford Coppola. "I don't feel scared of showing my dad scripts," she says. "He's so into films and young film-makers ­ he just loves it. And anyway, I think, if you like what you're doing, then it sort of doesn't matter what anyone else thinks."

ANGELINA JOLIE

The actress and her actor father, Jon Voight, have a tempestuous relationship. The Tomb Raider star once said that she was divorcing him: "I no longer see us as father and daughter. I won't have unhealthy relationships in my life." He, though, claims still to be crazy about his "Angie" and says: "Nothing is more important to me than my daughter's health and happiness."

KATE HUDSON

"I have zero problems when people say, 'God, you look like your mother,' " says Hudson, the daughter of Goldie Hawn. "I go: 'Well, great! Thanks!' " Kate is closer to her mother's long-term partner, Kurt Russell, than to her biological father, Bill Hudson. In 2003, the happy Hollywood family set up a production company, Cosmic Entertainment.